Angle Pairs Unit Test

Question

4 of 154 of 15 Items

Question
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=
°

Answer 1

Since the two adjacent angles form a resulting angle, we can set up an equation to find the unknown angle measures.

m∠1 + m∠2 = resulting angle measure
2x + (2x+7) = 135

Combining like terms:
4x + 7 = 135

Subtracting 7 from both sides:
4x = 128

Dividing by 4:
x = 32

Now we can substitute this value back into the equations for m∠1 and m∠2:

m∠1 = 2x = 2(32) = 64°
m∠2 = 2x+7 = 2(32)+7 = 71°

Therefore, the two unknown angle measures are:
m∠1 = 64°
m∠2 = 71°