Use the image to answer the 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

59°
59 degrees

31°
31 degrees

180°180 degrees
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1 answer

Since angles 1 and 2 form a right angle, we know that angle 1 + angle 2 = 90°.

We are given that angle 4 = 31°.

Since angles 3 and 4 both emerge from the same point, their sum must be 180°.

Therefore, angle 3 + angle 4 = 180°, which means angle 3 = 180° - angle 4 = 180° - 31° = 149°.

Since angles 2, 3, and 5 all form a straight line, their sum must be 180°.

Therefore, angle 2 + angle 3 + angle 5 = 180°, which means angle 2 = 180° - angle 3 - angle 5 = 180° - 149° - 0° = 31°.

So, m∠2 = 31°.