Use the image to answer the question.

Question

An illustration shows five rays emerging from an unlabeled point, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.

If m∠4=31° , what is m∠2 ?

(1 point)
Responses

59°
59 degrees

180°180 degrees

90°
90 degrees

31°
31 degrees
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Answer 1

To solve the problem, we need to use the information given:

1. Angles 1 and 2 together form a right angle, which means: \[ m∠1 + m∠2 = 90° \]

2. We know that \( m∠4 = 31° \). Since angles 3 and 4 are adjacent, they are supplementary: \[ m∠3 + m∠4 = 180° \] Thus, we can find \( m∠3 \): \[ m∠3 = 180° - m∠4 = 180° - 31° = 149° \]

3. Now, since angles 2 and 3 are adjacent and also supplementary, we can also find \( m∠2 \): \[ m∠2 + m∠3 = 180° \] Substituting \( m∠3 = 149° \): \[ m∠2 + 149° = 180° \] Solving for \( m∠2 \): \[ m∠2 = 180° - 149° = 31° \]

Thus, the measure of angle 2 is \( 31° \).

Therefore, the answer is: 31°.