Two adjacent angles, ∠1 and ∠2 , form a resulting angle with measure 135°. If m∠1=(2x)° and m∠2=(2x+7)°, what are the two unknown angle measures?(1 point) m∠1= °, m∠2=
m∠1 = 2x°
m∠2 = (2x + 7)°
Since the two angles are adjacent, their measures are added to give the resulting angle measure of 135°.
m∠1 + m∠2 = 135°
Substituting the given expressions for the angle measures:
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, the two angle measures are:
m∠1 = 2x = 2(32) = 64°
m∠2 = 2x + 7 = 2(32) + 7 = 71°
The unknown angle measures are m∠1 = 64° and m∠2 = 71°.