Answer:
a) see explanation below.
b) measure of ∠4 = 77°.
Step-by-step explanation:
Given a figure ∠4 is an exterior angle to ΔAUL.
a) We have to explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.
That is why ∠4 = ∠1 +∠2
Lets first ∠1 +∠2 = 52° +25° = 77°
angle sum property of triangle states that the sum of angles of a triangle is always equal to 180°.
Thus, ∠1 +∠2 + ∠3 = 180°
Substitute the know value and find the angle 3.
⇒ 77° + ∠3 = 180°
⇒ ∠3 = 180° - 77° = 103°
Also ∠3 + ∠4 = 180° (Linear pair )
⇒ ∠4 = 180° - 103° = 77°.
⇒ ∠4 = ∠1 +∠2
Thus, ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.
b) Measure of ∠4 = 77°.
