Answer: 131 degrees
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Work Shown:
Angles MQX and LQR are vertical angles, so they are equal to one another.
angle MQX = angle LQR
-4a+139 = 4a+123
-4a-4a = 123-139
-8a = -16
a = -16/(-8)
a = 2
Use this to find each angle
- angle MQX = -4a+139 = -4*2+139 = 131
- angle LQR = 4a+123 = 4*2+123 = 131
We get the same value 131 each time, so this confirms we have the correct value for 'a', and it confirms our answer for angle LQR.
