Question

Question
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

31°
31 degrees

90°
90 degrees

59°
59 degrees

180°

Answer 1

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

m∠1 + m∠2 = 90°

If m∠4 is given as 31°, and the angles around a point add up to 360°, we can express the relationship of the angles. The angles can typically be labeled as follows based on the ray structure:
- m∠1 and m∠2 are one pair forming a right angle,
- angles 3 and 4 form another pair adjacent to these, and
- angle 5 completes the set around the point.

From the information given, if m∠4 = 31°, then we can find m∠3 which is supplementary to m∠4:

m∠3 = 180° - m∠4 = 180° - 31° = 149°

Now, angles 1, 2, 3, and 4 must add up to 180° since they form a straight line. If we represent the remaining angle as m∠5, we know:

m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360°

To find m∠2, based on m∠1 + m∠2 = 90° and assuming m∠3 + m∠4 + m∠5 = 270°:

If we rearrange, we will have 90° (from m∠1 and m∠2) plus angles 3, 4, and 5 should give us 270°.

Given there are two angles (m∠1 and m∠2) summing to 90°, we can set:
m∠2 = 90° - m∠1.

We don't know ,m∠1 directly, but we can find that its logically related using previous information.

Thus, with m∠4 being provided as 31°, we would look from m∠1 + m∠2 = 90° and also using the rotational angles around the point and recognizing m∠2 would lead us into inferring possible options available:

Therefore, we can conclude m∠2 must be 59° in context with summation structures logically in mind.

So:

**m∠2 = 59°**