Question

In the figure, ∠6 is an exterior angle to (square) AUL.

A: Explain why m∠6 is equal to the sum of the measures of the two nonadjacent interior angles.
B: What is m∠6?
Answer:

Answer 1

Part A

• ∠6 + ∠3 = ∠PAL - angle addition
• ∠PAL = 180° - straight angle
• ∠6 + ∠3 = 180° - substitution
• ∠6 = 180° - ∠3 (1)

ΔAUL has

• ∠1 + ∠2 + ∠3 = 180° - property of triangles
• ∠1 + ∠2 = 180° - ∠3 (2)

(1) and (2) have RHS same, therefore LHS also same:

• ∠6 = ∠1 + ∠2

Part B

• ∠6 = ∠1 + ∠2 - given

Substitute measures

• ∠6 = 52° + 33°
• ∠6 = 85°