Two adjacent angles, angle 1 and angle 2, form a resulting angle with measure 135°. If angle 1=(2x)° and angle 2=(2x+7)°, what are the two unknown angle measures?
Since the two angles 1 and 2 are adjacent and form a resulting angle of 135°, we can set up the equation:
angle 1 + angle 2 = resulting angle
(2x)° + (2x+7)° = 135°
Combining like terms:
4x + 7 = 135
Subtracting 7 from both sides:
4x = 128
Dividing both sides by 4:
x = 32
Therefore, angle 1 = 2x = 2(32) = 64° and angle 2 = 2x + 7 = 2(32) + 7 = 71°.
The two unknown angle measures are 64° and 71°.