Answer:
Step-by-step explanation:
Find the diagram to the question attached. In line geometry, the <3 = <4 (oppositely directed angles are equal).
Given
<3 = 2x+23
<4 = 5x-112
Since they are both equal, we will equate the two function and get x:
2x+23 = 5x-112
Collect like terms
2x-5x = -112-23
-3x = -135
x = 135/3
x = 45°
Find the measure of each angle
For <3 = 2x+23
<3 = 2(45)+23
<3 = 90+23
<3 = 113°
For <4 = 5x-112
<4 = 5(45)-112
<4 = 225-112
<4 = 113°
As we can see, <3=<4= 113°. The theorem that justifies the work is oppositely directed angles are equal.
