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?
A. 59°
B. 90°
C. 31°
D.180°
If angles 1 and 2 form a right angle, then angle 2 is 90°. Since angle 4 is 31°, and angles 1 and 4 form a straight line, angle 1 is 180° - 31° = 149°. The sum of angles 1 and 2 is 149° + 90° = 239°.
Since the sum of angles 1, 2, 3, 4, and 5 is 360°, we can subtract the sum of angles 1, 2, 3, and 4 from 360° to find angle 5.
360° - 239° = 121°
Therefore, angle 5 is 121°.
Since the angles are formed in increasing order, angle 2 is between angles 1 and 3, and is therefore larger than both angle 1 (149°) and angle 4 (31°).
The only choice larger than both 149° and 31° is 180°, so m∠2 is D. 180°.