Question

A sprinkler swings back and forth between A and B in such a way that ∠1 ≅ ∠2, ∠1 and ∠3 are complementary, and ∠2 and ∠4 are complementary. sprinkler450 If m∠1 = 34.5°, find m∠2, m∠3, and m∠4. The measure of ∠2 is 34.5 °. The measure of ∠3 is 111 °. The measure of ∠4 is 111 °.

Answer 1

Answer: - m∠1 = 34.5°

- m∠2 = 34.5°

- m∠3 = 55.5°

- m∠4 = 55.5°

Explanation:

Given the information provided, we can find the measures of ∠2, ∠3, and ∠4 as follows:

1. We're given that ∠1 ≅ ∠2, and m∠1 = 34.5°. So, m∠2 is also 34.5°.

2. We know that ∠1 and ∠3 are complementary, which means their measures add up to 90°. Since m∠1 = 34.5°, we can find m∠3 as follows:

m∠1 + m∠3 = 90°

34.5° + m∠3 = 90°

m∠3 = 90° - 34.5°

m∠3 = 55.5°

3. We also know that ∠2 and ∠4 are complementary, which means their measures add up to 90°. Since m∠2 = 34.5°, we can find m∠4 as follows:

m∠2 + m∠4 = 90°

34.5° + m∠4 = 90°

m∠4 = 90° - 34.5°

m∠4 = 55.5°

So, the measures of the angles are as follows:

- m∠1 = 34.5°

- m∠2 = 34.5°

- m∠3 = 55.5°

- m∠4 = 55.5°