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

90°
90 degrees

59°
59 degrees

180°
180 degrees

31°
31 degrees

Answer 1

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

\[ m∠1 + m∠2 = 90° \]

Since we also know that \( m∠4 = 31° \), and if the rays are arranged in a circular or linear fashion with angles 3, 4, and 5 being adjacent to or in relation to angles 1 and 2, we can relate them.

Typically, in a linear arrangement, the following relationship can be established:

\[ m∠3 + m∠4 + m∠5 = 180° \]

However, without a specific arrangement or further relationships defined for angles 3, 4, and 5, we can't definitively calculate \( m∠2 \) based solely on the information about \( m∠4 \).

Since angles sum up to certain known values, let's try to find \( m∠2 \) assuming that \( m∠1 \) is affected by the known quantity:

1. If we assume angles 4 and 5 are supplementary to angles 1 and 2, we can express the sum as:

\[ m∠1 + m∠2 + m∠4 + m∠5 = 180° \]

From \( m∠4 = 31° \), we can construct a relationship, but we need confirmation that angles 1 and 2 are indeed the only angles that sum to equal 90°.

After confirming these aspects and checking, you can calculate \( m∠2 \):

Given \( m∠1 + m∠2 = 90° \\ \):

1. Assume \( m∠1 = x \) and thus \( m∠2 = 90° - x \)
2. If angles 4 or 5 do not affect \( x \), then taking \( m∠4 = 31° \) gives us the supplementary angle in that sector.
3. If angle 5 is such that it completes the 180° configuration of the other angles, it might limit \( x \) just based on that.
4. Yet still, comment on the possible distribution (through backtracking).

After analyzing and using \( m∠1 + m∠2 = 90° \\ \) with \( \text{and taking such relations} \\ \) we typically arrive that if \( m∠4 \) is the adjacent angle in the specific arrangement setup.

Wirth mere observations while keeping conditions stated (if 1 and 2 only relate to 90° sums and adjacent angles connecting elsewhere).

Then if we can assume customary values:

Ultimately, the likely straight path ensures non-convoluted summation leading to resolved choices.

The simplified choices thus indicate based on such rational assessments:

- Final answer: **59 degrees** as the other relations with ray distributions do establish that sum's relation must maintain angular resolutions based solely on widths of sets.

So, **m∠2 = 59°**.