Question

Find the value of each variable and the measure of each labeled angle.

Answer 1

Answer: (5x)°=(8x-75)°=125°

Explanation:

Property of vertical angles: vertical angles are equal

Hence,

`(8x-75)^0=(5x)^0\\(8x)^0-75^0=(5x)^0\\(8x)^0-75^0-(5x)^0=(5x)^0-(5x)^0\\(3x)^0-75^0=0\\(3x)^0-75^0+75^0=0+75^0\\(3x)^0=75^0\\`

Divide both parts of the equation by 3 :

`x^0=25^0\\(5x)^0=(5*25)^0\\(5x)^0=125^0`

Answer 2

see explanation

Explanation:

(8x - 75) and (5x) are vertically opposite angles and are congruent , then

8x - 75 = 5x ( subtract 5x from both sides )

3x - 75 = 0 ( add 75 to both sides )

3x = 75 ( divide both sides by 3 )

x = 25

Then

5x = 5(25) = 125°

8x - 75 = 8(25) - 75 = 200 - 75 = 125°