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.

Question

If m∠4=31° , what is m∠2 ?

Answer 1

Since angles 1 and 2 together form a right angle, the measure of angle 1 plus the measure of angle 2 is 90 degrees. So, m∠1 + m∠2 = 90°.

Since m∠4 = 31°, this means that the measure of angle 3 is 180° - 31° = 149°.

Since angles 3 and 4 form a straight line, their measures must add up to 180 degrees, so m∠3 + m∠4 = 180°. Therefore, m∠3 = 180° - 31° = 149°.

We now have the measures of all 5 angles:
m∠1 = 90° - m∠2
m∠2 = m∠2
m∠3 = 149°
m∠4 = 31°
m∠5 = ?

Since angles 1 and 2 together form a right angle, their measures must add up to 90 degrees, so m∠1 + m∠2 = 90°. Therefore, we have 90° - m∠2 + m∠2 = 90°.

This means that m∠2 = 90°.

Therefore, the measure of angle 2 is 90 degrees.

Answer 2

it's 59. 4 is vertical to 1, and 1 and 2 make a right angle which is 90 degrees.
90-31 is 59.

Answer 3

Apologies for the confusion in my previous response. You are correct.

Since angle 4 is vertical to angle 1, and angles 1 and 2 form a right angle, we can conclude that angle 2 is equal to 90° - 31° = 59°.

Therefore, the measure of angle 2 is 59 degrees.

Answer 4

An illustration shows two parallel slanting lines m and l intersecting a vertical line k. The angles formed at the intersection of lines l and k are 1, 2, 4, and 3. The angles 1 and 4 are opposite to each other while angles 2 and 3 are opposite to each other. The angles formed at the intersection of lines m and k are 5, 6, 8, and 7. The angles 5 and 8 are opposite to each other while angles 6 and 7 are opposite to each other.
If m∠6=140° , what is m∠7 ?

Answer 5

Since angles 6 and 7 are opposite to each other, their measures must be equal. Therefore, m∠7 = m∠6 = 140°.

Therefore, the measure of angle 7 is 140 degrees.