Question

unit 2 test- points, lines, and planes, and constructions
name:

1. points x, y, and z are collinear. 5pts

what is x?

1. use the figure to identify each. 2 pts per blank

a) name an adjacent angle to ∠1?
b) name an angle congruent to ∠1?
c) name an angle supplementary to ∠1?

1. line $\boldsymbol{ell}$ is parallel to line m. given $mangle1 = 115^circ$, find each measure and give the relationship to ∠1 .

d) $mangle8 =$ ______ because ∠8 is ______ to ∠1.
e) $mangle5 =$ ______ because ∠5 is ______ to ∠1.
f) $mangle4 =$ ______ because ∠4 is ______ to ∠1.

1. list the type of angles that are labeled.

then find the value of x.
type of angle: ________
$x =$ ________

1. list the type of angles that are labeled.

then find the value of x.
type of angle: ________
$x =$ ________

1. the equation of line b is $y=-3x + 12$ and the equation of line q is $y=6x - 8$. are those lines parallel, perpendicular or neither?

slope line 1 | slope line 2 | type of lines

1. write the equation of the line that is perpendicular to $y = -\frac{1}{3}x + 5$ and passes through (3,-4).
2. what is the slope of a line that is parallel to the line $y=\frac{3}{2}x + 4$

b) 2/3 b)-3/2 c) -2/3 d) 3/2

1. what is the slope of the line perpendicular to $y= -3x + 2$

b) 3 b) 2 c)1/3 d) -1/3

Explanation:

Step1: Set linear pair equation

$\angle XYW + \angle WYZ + \angle ZYX = 180^\circ$, so $(3+5x)+(x+15)+(3+5x)=180$

Step2: Simplify the equation

$3+5x+x+15+3+5x=180 \implies 11x+21=180$

Step3: Solve for x

$11x=180-21 \implies 11x=159 \implies x=\frac{159}{11}\approx14.45$

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Step1: Identify adjacent angle to $\angle1$

Adjacent angles share a side/vertex: $\angle2$ (or $\angle3$)

Step2: Identify congruent angle to $\angle1$

Vertical angles are congruent: $\angle4$

Step3: Identify supplementary angle to $\angle1$

Linear pairs are supplementary: $\angle2$ (or $\angle3$)

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Step1: Find $m\angle8$

$\angle8$ is corresponding to $\angle1$: $m\angle8=115^\circ$

Step2: Find $m\angle5$

$\angle5$ is alternate exterior to $\angle1$: $m\angle5=115^\circ$

Step3: Find $m\angle4$

$\angle4$ is same-side interior to $\angle1$: $m\angle4=180^\circ-115^\circ=65^\circ$

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Step1: Identify angle type

Corresponding angles (parallel lines, transversal)

Step2: Set equal angles equation

$4+32x=25x+5$

Step3: Solve for x

$32x-25x=5-4 \implies 7x=1 \implies x=\frac{1}{7}\approx0.14$

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Step1: Identify angle type

Alternate exterior angles (parallel lines, transversal)

Step2: Set equal angles equation

$8x+15=9x+7$

Step3: Solve for x

$15-7=9x-8x \implies x=8$

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Step1: Find slopes of lines

Slope of Line b: $-3$; Slope of Line q: $6$

Step2: Classify line relationship

Not equal, product $
eq-1$: Neither parallel nor perpendicular

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Step1: Find perpendicular slope

Perpendicular slope to $-\frac{1}{3}$ is $3$

Step2: Use point-slope form

$y-(-4)=3(x-3)$

Step3: Simplify to slope-intercept

$y+4=3x-9 \implies y=3x-13$

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Step1: Identify parallel slope

Parallel lines have equal slopes: $\frac{3}{2}$

Step2: Match to option

Option D) $\frac{3}{2}$

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Step1: Find perpendicular slope

Perpendicular slope to $-3$ is $\frac{1}{3}$

Step2: Match to option

Option C) $\frac{1}{3}$

Answer:

1. $x=\frac{159}{11}\approx14.45$
2. a) $\angle2$ (or $\angle3$); b) $\angle4$; c) $\angle2$ (or $\angle3$)
3. d) $115^\circ$, corresponding; e) $115^\circ$, alternate exterior; f) $65^\circ$, same-side interior
4. Type of angle: Corresponding angles; $x=\frac{1}{7}$
5. Type of angle: Alternate exterior angles; $x=8$
6. | Slope line 1 | Slope line 2 | Type of Lines |

$-3$

$6$

Neither

1. $y=3x-13$
2. D) $\frac{3}{2}$
3. C) $\frac{1}{3}$