a sprinkler swings back and fourth between A and B in such a way that <1 is congruent to <2. <1 and <3 are complemen

Question

3 years ago

10

tary, and <2 and <4 are complementary. If m<1=47.5 degress, find m<2, m<3, and m<4

1 answer:

LekaFEV [45] · Answer 1 · 2022-03-02T15:52:56+03:00

Answer:

m∠2=47.5°

m∠3=42.5°

m∠4=42.5°

Step-by-step explanation:

We are given in the question that m∠1=47.5 degrees=47.5°.

" Angles are congruent if they have the same angle measure in degrees" ----(1)

As we are given that ∠1 is congruent to ∠2.

This implies from statement (1) that:

m∠2=47.5 degrees=47.5°

" Complementary Angle: Two Angles are Complementary when they add up to 90 degrees (a Right Angle)."

In the question we are given ∠1 and ∠3 are complementary.

This means ∠1+∠3=90°

⇒ ∠3=90°-∠1

⇒ ∠3=90°-47.5°=42.5°

Hence, m∠3=42.5°

Also we are given that ∠2 and ∠4 are complementary.

This means ∠2+∠4=90°

⇒ ∠4=90°-∠2

⇒ ∠4=90°-47.5°=42.5°

Hence, m∠4=42.5°.