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

90°
90 degrees

31°
31 degrees

180°
180 degrees

59°

Answer 1

Since angles 1 and 2 together form a right angle, we know that:

m∠1 + m∠2 = 90°

Given that m∠4 is 31°, we can identify that angles 3 and 4 must sum to 180° (as they are supplementary angles). Therefore:

m∠3 + m∠4 = 180° m∠3 + 31° = 180° m∠3 = 180° - 31° m∠3 = 149°

Now, knowing the relationships between the angles, angles 2 and 3 should also be supplementary:

m∠2 + m∠3 = 180° m∠2 + 149° = 180° m∠2 = 180° - 149° m∠2 = 31°

So, the measure of angle 2 (m∠2) is 31°.

The correct response is: 31°