Asprinkler swings back and fourth between a and b in such a way that < 1 is congruent to < 2. < 1 and < 3 are complementary, and < 2 and < 4 are complementary. if m< 1=47.5 degress, find m< 2, m< 3, and m< 4

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°.

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step-by-step explanation: