Question

relationships continued
use the angle relationships shown in each diagram to complete the equations.
12 (3x = 135), (x = 45)
13 (4x + 12=112), (x = 25)
15 what term refers to the pair of labeled angles? are these angles congruent? if so, find the value of x. if not, explain why not.

Explanation:

Step1: Identify angle - pair relationship

The two angles are vertical angles. Vertical angles are congruent. So we set up the equation based on the equality of the two vertical - angle measures.
$10x−19 = 67$

Step2: Solve the equation for x

First, add 19 to both sides of the equation:
$10x−19 + 19=67 + 19$
$10x=86$
Then, divide both sides by 10:
$x=\frac{86}{10}=8.6$

Answer:

The term for the pair of labeled angles is vertical angles. They are congruent and $x = 8.6$