Question

geometry find the measurement of the exterior angle. in the image below, new path and east path are parallel. find the measure of: w ____ x __ y __ z __ expressions and equations boxes that are the same size and shape must have the same number in them. after solving the balance, write an equation for it. ratios, proportions and percents 100% 50% 25% 10% 5% 2 1/2% 1% 200 a) 75% x 200 = __ b) 35% of 200 is __ c) 15% x 200 = __ d) 60% of 200 is __ e) 49% x 200 = __ f) 55% of 200 is __ g) 30% x 200 = __ h) 20% of 200 is __ i) 500% x 200 = __ j) 2% of 200 is ____ which television would cost you less money? a $429 television set with a 20% discount or a television set with no discount priced at $359? graphing prove these shapes are congruent using a sequence of transformations. write and draw the transformations. be specific.

Explanation:

Step1: Find exterior - angle of triangle

The sum of the two non - adjacent interior angles of a triangle is equal to the exterior angle. Given interior angles 73° and 62°.
$x=73 + 62$
$x = 135$

Step2: Calculate percentage values

a) $75\%\times200=\frac{75}{100}\times200 = 150$
b) $35\%\text{ of }200=\frac{35}{100}\times200=70$
c) $15\%\times200=\frac{15}{100}\times200 = 30$
d) $60\%\text{ of }200=\frac{60}{100}\times200 = 120$
e) $49\%\times200=\frac{49}{100}\times200 = 98$
f) $55\%\text{ of }200=\frac{55}{100}\times200 = 110$
g) $30\%\times200=\frac{30}{100}\times200 = 60$
h) $20\%\text{ of }200=\frac{20}{100}\times200 = 40$
i) $500\%\times200=\frac{500}{100}\times200 = 1000$
j) $2\%\text{ of }200=\frac{2}{100}\times200 = 4$

Step3: Find angles with parallel lines

Since New Path and East Path are parallel, $w = 72^{\circ}$ (corresponding angles). $x=47^{\circ}$ (corresponding angles). $y = 47^{\circ}$ (alternate interior angles with $x$). $z = 72^{\circ}$ (alternate interior angles with $w$)

Step4: Solve balance equation

Let the number in each box be $n$. For the first balance: $5n=41$, so $n=\frac{41}{5}=8.2$. For the second balance: $4n = 26$, so $n=\frac{26}{4}=6.5$

Step5: Compare TV prices

For the $429$ TV with 20% discount, the discount amount is $0.2\times429 = 85.8$. The sale price is $429-85.8=343.2$. Since $343.2<359$, the $429$ TV with 20% discount costs less.

Step6: Prove congruence of shapes

Translate the shape $QRST$ 6 units to the left and 3 units down to map it onto $Q'R'S'T'$.

Answer:

Exterior angle of triangle: 135°
a) 150
b) 70
c) 30
d) 120
e) 98
f) 110
g) 60
h) 40
i) 1000
j) 4
$w = 72^{\circ}$, $x = 47^{\circ}$, $y = 47^{\circ}$, $z = 72^{\circ}$
First balance: $5n = 41$; Second balance: $4n = 26$
The $429$ TV with 20% discount costs less.
Translate shape $QRST$ 6 units left and 3 units down to prove congruence.