Answer :
The measure of Angle 4; m∠4 = 40°.
Define angle.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Angles 6 and 7 are vertical angles that are opposite to each other. As vertical angles are congruent:
11x + 8 = 12x - 4
11x - 12x = -4 - 8
-x = -12
Therefore, x = 12
Now,
m angle 6 = (11 * 12 + 8)° =140°
m angle 7= (12 * 12 - 4)° = 140°
Angles 6 and 8 are supplementary angles that add up to 180°
Therefore,
m angle 8= 180° - 140° = 40°
Angles 8 and 4 are corresponding angles, As corresponding angles are congruent:
m angle 4= 40°
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