Two adjacent angles, ∠1 and ∠2, form a resulting angle that measures 135° . If m ∠1 = (2x)° and m∠2 = (2x + 7)° , what are the two unknown angle measures?
m∠1 = ____
m∠2 = ____
A. 32
B. 64
C. 71
D. 158
We know that the sum of ∠1 and ∠2 is equal to the resulting angle, which measures 135°. Therefore, we can set up the equation:
m∠1 + m∠2 = 135
Substituting the given expressions for m∠1 and m∠2 into the equation, we get:
(2x) + (2x + 7) = 135
Combining like terms, we have:
4x + 7 = 135
Subtracting 7 from both sides, we get:
4x = 128
Dividing both sides by 4, we find:
x = 32
Therefore, m∠1 = 2x = 2(32) = 64° and m∠2 = 2x + 7 = 2(32) + 7 = 71°.
The two unknown angle measures are:
m∠1 = 64°
m∠2 = 71°
The correct answer is option C.