Question

PLEASE HELP!!

In the figure, ∠4 is an exterior angle to [] AUL .

(a) Explain why m∠4 is equal to the sum of the measures of the two nonadjacent interior angles.
(b) What is m∠4 ?

Answer 1

In the figure, ∠4 is an exterior angle to AUL.

∠4 = 77°

∠4 = ∠1 +∠2

∠1 +∠2 = 52° +25° = 77°

Substitute the value that we alreay know to find ∠3.

⇒ 77° + ∠3 = 180°

⇒ ∠3 = 180° - 77° = 103°

∠4 is equal to the measures of two nonadjacent interior angles, the sum of angles is always 180° so ∠1 +∠2 + ∠3 = 180°. In summary ∠4=sum of the measures of the two nonadjacent interior angles.

Hope this helps, have a BLESSED AND WONDERFUL DAY! As well as a great Black History Month and Valentine's day! :-)

- Cutiepatutie ☺❀❤

Answer 2

a) Here, sum of two non-adjacent angles: 52 + 25 = 77
Now, ∠3 = 180 - 77 [ sum of all angles in a triangle is 180 ]
so, ∠3 = 103

Now, ∠3 + ∠4 = 180 [ Supplementary angles ]
So, ∠4 = 180 - ∠3
∠4 = 180 - 103 = 77
∠4 = 77 [ which is sum of two non-adjacent angles ]

....Hence proved.

b) m∠4 = 77
[ Solved in previous section ]

Hope this helps!