Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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find the measure of each interior angle and each exterior angle of a re…
Measure of each interior angle \(=\boxed{150}\)° Measure of each exterior angle \(=\boxed{30}\)°
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find the measure of each interior angle and each exterior angle of a re…
Measure of each interior angle = \(162^{\circ}\) Measure of each exterior angle = \(18^{\circ}\)
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the parallelogram ghij is a dilation of the parallelogram ghij. what is…
\( \frac{5}{4} \)
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drag the red vertical line to find the y-values: orange graph: when x=1…
Orange graph: \( y = -1 \) (assuming the line is \( y = x - 2 \)) Blue graph: \( y = 1 \) (assuming the upper part of the curve) (Note: The actual values may depend on the exact g…
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why government? b. venn diagram. put the number of the word in the righ…
To solve this Venn diagram problem, we analyze each concept and assign it to the correct category (State of Nature, Social Contract, or both) based on the definitions of these pol…
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section 12.1.12.2 cfu integrated math 2 - version d 1. classify the fol…
1. Acute scalene triangle 2. $x = 59$ 3. $x = 37$, $y = 61$
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similar by: aa ~ aixz - aqex similar by: afny - rwt similar by:
\( \triangle FNY \sim \triangle RWY \) por SAS (Lado - Ángulo - Lado)
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13. find the value of x so that ℓ ∥ m. (7x + 15)° ℓ m 25° n
\( x = 20 \)
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lines k, l, m with angles (3x + 10)° and (5x + 18)° as shown in the ima…
If we are to find \( x \), then \( x = 19 \)
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suppose we are given the following. line 1 passes through $(-3, -4)$ an…
Slope of Line 1: \(\frac{2}{3}\) Slope of Line 2: \(\frac{3}{2}\) Slope of Line 3: \(\frac{3}{2}\) ### Part (b)
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11. there is a diagram with three lines: line k (a transversal) interse…
\( x = 7 \)
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suppose we are given the following. line 1 passes through (4, -1) and (…
### Part (a) To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). #### Slope of …
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question 2 math8: chapter 4 test positive negative zero undefined
- positive ↔ top graph (line rising left to right) - negative ↔ second graph (line falling left to right) - zero ↔ bottom graph (horizontal lines) - undefined ↔ third graph (verti…
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10. there is a diagram with two parallel lines ( l ) and ( m ), and a t…
\( x = 2 \)
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7. determine if the triangles are similar. if similar, state how and co…
The triangles are similar by AA (Angle - Angle) similarity. The similarity statement is \( \triangle LMN \sim \triangle LGH \) (or appropriate labels) by AA. ### Problem 8:
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in the diagram, lines l, m are parallel, and line k is a transversal. t…
\( x = 20 \)
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amending the constitution - multiple choice questions circle the correc…
1. d. By adding an amendment to it 2. d. Cannot be changed 3. c. Both a. and b. above 4. d. None of the above 5. d. None of the above 6. a. The Bill of Rights
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example 2 find the value of x so that ℓ || m. 7. image of two parallel …
\( x = 22 \)
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name: ______________________________ date: ______ the articles of the c…
1. a. The Congress 2. c. 6 years 3. b. Create states 4. d. Three-quarters 5. d. The Constitution 6. a. At the beginning
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in the geometric figure, there are triangles with segments labeled: ge …
$x = 9$
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5. find the value of x. 6. find the value of x. 3. if l, m, and n are t…
a) $LM = 23$ b) $MN = 20$ c) $QR = 34$ d) $MR = 17$ --- ### Problem 4:
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questions: how a bill becomes a law circle the correct answer 1. which …
1. A. someone has an idea for a law 2. D. sponsor 3. A. a committee 4. D. all of the above 5. C. is ready for vote
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2. given: ∠s ≅ ∠v, t is the midpoint of \\(\\overline{sv}\\). prove: \\…
$\triangle RTS \cong \triangle UTV$ is proven by the ASA Congruence Postulate.
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3. if the figures below are similar, find the scale factor of figure b …
\( \frac{1}{3} \)
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read the statement: \if a triangle is isosceles, then its base angles a…
A. If the base angles of a triangle are not congruent, then the triangle is not isosceles.
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what is the area of the sand mandala? use 3.14 for \\(\\pi\\).\\(a = \\…
\( 0.785 \) square meters
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find the slope of the line $y = \\frac{2}{3}x - \\frac{3}{4}$. simplify…
$\frac{2}{3}$
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statements 1. draw \\(\\overline{ad}\\), the angle bisector of \\(\\ang…
Definition of angle bisector ### For Statement 5:
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5. an equilateral triangle has side length 8 units. what is the area? a…
A. $16\sqrt{3}$ square units
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a manufacturer cuts a piece of metal for a microscope. the resulting pi…
\(AB=\boldsymbol{\sqrt{73}}\) mm, \(BC=\boldsymbol{\sqrt{73}}\) mm, \(AC = \boldsymbol{6}\) mm. Since \(AB = BC\), \(\triangle ABC\) is isosceles.
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10. given: $bc \\parallel ef$, $\\overline{ab} \\cong \\overline{de}$, …
$\triangle ABC \cong \triangle DEF$ is proven by the AAS congruence postulate.
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2. the ratio of the measures of the sides of a triangle is 9:7:3. if th…
42 inches
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6. what is the side length in this square? a. 3 units b. \\(\\frac{6}{\…
B. $\frac{6}{\sqrt{2}}$ units
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11. given: ∠s ≅ ∠u, and \\(\\overline{tr}\\) bisects ∠stu prove: \\(\\t…
$\triangle SRT \cong \triangle URT$ is proven by the AAS Congruence Theorem.
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sawyer is grounded and has to stay in his room all day. he made up a ga…
18.84
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4. given: $overline{cd}$ bisects $overline{ae}$, $overline{ab} parallel…
$\triangle ABC \cong \triangle CDE$ is proven by the AAS congruence criterion.
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javier is grounded and has to stay in his room all day. he made up a ga…
2
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(a) use the number line to find the distance between -1 and 7. distance…
(a) 8 (b) $-1 -7 = -8$; $7 - (-1) = 8$ (c) $|-1 -7| = 8$; $|7 - (-1)| = 8$
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1. the ratio of the measures of the three angles in a triangle is 14:5:…
Las medidas de los ángulos son \( 84^\circ \), \( 30^\circ \) y \( 66^\circ \).
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8. this diagram shows the design for a quilt. the quilt is made of 4 sq…
a. $2$ b. $8$
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which formulas can be used to find the circumference of a circle? choos…
\( C = 2\pi r \), \( C=\pi d \)
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solve for ( x ). round your answer to the nearest tenth if necessary. f…
\(x\approx33.8\)
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for each graph, decide if the two lines are parallel, perpendicular, or…
Graph 1: Perpendicular Graph 2: Neither Graph 3: Parallel Graph 4: Parallel
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find the area of the circle. use your calculator’s value for $\\pi$. ro…
The area of the circle is approximately \( 149.57 \) square yards. ### Problem 70:
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examine rectangle jklm, shown below image of rectangle jklm with diagon…
- \( NM = 8 \) - \( JL = 16 \)
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at any instant, $m\\angle d = 35^\\circ$ and $m\\angle c = (4x + 5)^\\c…
x = 7.5, m∠A = 55, AB = 35, BC = 24.5 (but maybe the intended answers are x = 7.5, m∠A = 55, AB = 35, BC = 35? No, that's conflicting. Wait, maybe the problem is x = 7.5, m∠A = 55…
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67.) triangle with base - related side 3 m and height 1.9 m 68.) triang…
The area of the triangle in problem 67 is $2.85$ square meters. ### For Problem 68 (Triangle with base 6 ft and height 4 ft)
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30° 60° 90° special right triangles 1. find and label the measure of ea…
1. Missing angles: - Triangle ABC: $\angle C = 60^\circ$ - Triangle XYZ: $\angle Z = 60^\circ$ - Triangle QRS: $\angle Q = 30^\circ$ 2. For all triangles, the hypotenuse is **2 ti…
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solve for ( x ). round your answer to the nearest tenth if necessary. f…
\(29.0\)
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question 1-10 a square pqrs has vertices p(2, 4), q(6, 8), r(10, 4) and…
The fourth option (the one with Step 1: Find the slope of diagonal \(PR\) (\(m_1\)) and slope of diagonal \(QS\) (\(m_2\)); Step 2: Show that \(m_1\times m_2 = - 1\))
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65.) rectangle with length 10.4 yd and width 6 yd 66.) rectangle with l…
The area of the rectangle is \( 62.4 \) square yards. ### Problem 66 (Area of Rectangle)
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step 1 statement rstu is a parallelogram 2 \\(\\overline{rs}\\) is para…
- symmetric property - definition of a parallelogram - alternate interior angles are congruent - corresponding parts of congruent triangles are congruent
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1 ( ab cong cd ); ( ab parallel cd ) given 2 ( angle bac cong angle dca…
C. Reason 5 should be "Corresponding parts of congruent triangles are congruent." (Assuming the third option is labeled C; if the original options had labels like A, B, C as per t…
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question 1-7 the quadrilateral wxyz is a square. the coordinates of the…
- Side \(WX\): \(\frac{1}{8}\) - Side \(XY\): \(-8\) - Side \(YZ\): \(\frac{1}{8}\) - Side \(ZW\): \(-8\)
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find the area of the polygon. do not forget about the proper unit notat…
\( 121\) square feet (or \( 121\space ft^2\)) ### Problem 64:
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4 what is the area of regular hexagon abcdef? explain or show your reas…
2340
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examine parallelogram abcd below. determine which of the following valu…
# Explanation: ## Step1: Recall parallelogram angle property In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)), and opposite angles are equal. Here, …
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two parallel sides, \\(\\overline{ab}\\) and \\(\\overline{cd}\\), of t…
6.4 units
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figure abcd is the image of figure abcd after a rotation around point e…
$45^{\circ}$
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which name does not describe this shape? parallelogram quadrilateral re…
rectangle
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what term describes the section between points a and d?
The term that describes the section between points A and D is a **line segment** (or simply "segment"). However, more precisely, since the figure is a line (with arrows on both en…
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which best describes one way to show \\(\\frac{1}{3}\\) shaded? draw a …
C. Draw a circle and cut it into 3 equal parts. Shade 1 part. (assuming the options are labeled A, B, C, D in the order they appear, with the third option being C)
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which pair of lines are parallel?
The pair of lines in the bottom - right figure (the last figure with two arrows having the same slope and direction) are parallel.
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theorem 7.2 polygon exterior angles theorem the sum of the measures of …
\( x = 68 \) ### Example 6: #### (a) Interior Angle of Regular Dodecagon
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1. the volume, v, of a rectangular pyramid can be determined by the for…
$\boldsymbol{w = \frac{3V}{lh}}$ (the first option)
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what is the equation of the line in standard form? 3x + y = 6 3x - y = …
$\boldsymbol{x - 6y = -9}$
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using the pencil, plot the point (4, -1).
The point is plotted at the intersection of the vertical line $x=4$ and horizontal line $y=-1$, 4 units right of the origin and 1 unit below the origin.
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example 4 finding angle measures in polygons a home plate for a basebal…
The polygon is not regular. A regular polygon requires all sides to be congruent and all interior angles to be congruent. The home - plate pentagon has two right angles (\(\angle …
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which is true about triangles abc and def? graph with triangles abc and…
The triangles are similar because $\frac{12-6}{4-2} = \frac{27-15}{9-5}$
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zero slope positive slope undefined slope negative slope (graph from ma…
Negative Slope
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positive slope zero slope undefined slope negative slope
Zero Slope
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options: positive slope, undefined slope, zero slope, negative slope. c…
A. Positive Slope
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of each triangle. round your answers to the 2) 6.9 in 6.5 in x
9.5 inches
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4. using the figure and the given statement in example 3, prove that $\…
\( \angle C \) and \( \angle F \) are supplementary (proven via substitution and angle - relationship postulates from Example 3). The two - column proof above shows the logical st…
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graph the line. $y = -\\frac{1}{3}x + 2$
# Explanation: ## Step1: Identify the y - intercept The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-\…
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metry missing sides ( side, x. geometry © 2022 kuta software llc. all r…
$8.3$ ft
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find the measures of the sides of $\\triangle jkl$, then classify it by…
21. Longitudes: $JK=2\sqrt{17}$, $KL=2\sqrt{17}$, $JL=6\sqrt{2}$; Clasificación: Triángulo isósceles 22. Longitudes: $JK=\sqrt{41}$, $KL=\sqrt{85}$, $JL=\sqrt{130}$; Clasificación…
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8. a convex hexagon has exterior angles with measures 34°, 49°, 58°, 67…
The measure of the exterior angle at the sixth vertex is \( 77^\circ \). ### Question 9
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directions: review the information below. type your answer in the space…
108 $\text{cm}^3$
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what is the value of p? triangle image with right angle, two 45° angles…
$p = 22\sqrt{2}$ (Option 3)
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a scale drawing of a building needs to be made using the scale 1 in = 2…
10
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a scale drawing of a building needs to be made using the scale 1 in = 1…
10
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the figures shown are similar. find the lengths of x, y, and z. the len…
12
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what is the interior angle sum of a heptagon? 900 540 1080 720
900
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the figures shown are similar. find lengths of x, y, and z. the length …
16
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core was the congress on racial equality. it was founded in 1942 and be…
The purpose of this document is to provide practical examples, training materials (like workshops and role - playing scenarios), and guidance on nonviolent action for civil rights…
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(continued) e. if \\(\\frac{x}{z} = 0.7\\), what is the measure of \\(\…
Question 6: $44^\circ$ Question 7: $b\sqrt{2}$ cm
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which point is not on the circle with center (3,2) and radius 5? (8, -2…
A. (8, -2), C. (3, 6)
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jared is creating a flower garden in the shape of a triangle. which cou…
3 by 7 by 9
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two students draw shaded figures to represent the fraction \\(\\frac{1}…
C. Only Remi is correct.
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the figure is shaded to represent a fraction of a whole. figure: a squa…
D. \(\frac{3}{4}\)
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6. here are two right triangles. a. explain how you know the right tria…
a. Both are right triangles with shared acute angle $\alpha$, so by AA similarity, they are similar. b. $\frac{r}{q}$ c. $\frac{y}{x}$ and $\frac{r}{q}$ d. Similar triangles have …
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which of these letters have point symmetry? o m x c f z □ m □ x □ o □ c…
X. X, O. O, Z. Z
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given the image below, which statement must be true? options: - only ( …
Both \(a \parallel b\) and \(c \parallel d\)
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ten words in context in the space provided, write the letter of the mea…
1. B. unsure. 2. C. full of joy. 3. B. to run into. 4. A. to grow gradually. 5. B. an error. 6. A. unreal.
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triangle klm is shown below. image of triangle klm with angle at m bein…
$\overline{MK}, \overline{ML}, \overline{KL}$
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2. translate the following statements into coordinate points, then plot…
- a. Coordinate point: \( (-1, 1) \) - b. Coordinate point: \( (2, 7) \) - c. Coordinate point: \( (1, -1) \) - d. Coordinate point: \( (3, 0) \) (For plotting, use the coordinate…
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2. based on the figure, select all true equations. a (cos(45^circ) = a)…
b. $\cos(48^\circ) = \frac{b}{c}$ c. $\sin(48^\circ) = \frac{a}{c}$ e. $\tan(48^\circ) = \frac{a}{b}$
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a diagonal walkway cuts through a park bordered by two parallel streets…
42
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self-assessment 3. the sum of the measures of the interior angles of a …
The polygon is a decagon (a 10 - sided polygon).