Vertical Angles Quick Check

Question

4 of 54 of 5 Items

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

59°
59 degrees

180°
180 degrees

90°
90 degrees

31°
31 degrees
Skip to navigation

page 11 of 11

Answer 1

In the given scenario, angles 1 and 2 form a right angle, which means their measures add up to 90 degrees.

Since you mentioned that \( m∠4 = 31° \), this means that angle 4 is adjacent to angle 3, and hence angles 3 and 4 together form another pair of vertical angles with angle 2.

Since angles 4 and 3 are adjacent angles along a straight line, they add up to 180 degrees (straight line).

Thus: \[ m∠2 + m∠4 = 90° \] \[ m∠2 + 31° = 90° \]

To find \( m∠2 \): \[ m∠2 = 90° - 31° \] \[ m∠2 = 59° \]

So, the correct answer is: 59°.