Applying the vertical angles and triangle sum theorem, we have:
angle b + angle c = 56 + 56 = 112°
angle b + angle e = 56 + 12 = 68°
angle e + angle c = 12 + 56 = 68°
How to Apply the Vertical Angles Theorem and the Angles on a Straight line Theorem?
Based on the angles on a straight line theorem, we have the following:
e + 44 + 124 = 180
e + 168 = 180
e + 168 - 168 = 180 - 168
e = 12°.
Each interior angle in a rectangle is 90 degrees. Therefore:
b + 34 = 90
b = 90 - 34
b = 56°.
a = 46° based on the vertical angles theorem
d + 102 = 180 [angles on a straight line theorem]
d = 180 - 102
d = 78°
c = 180 - a - d [triangle sum theorem]
Substitute
c = 180 - 46 - 78
c = 56°
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