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?

Question

use base:

m∠1=
m∠2=

Answer 1

m∠1 = 2x°
m∠2 = (2x + 7)°

Since the two angles are adjacent, their measures can be added together to give the resulting angle measure of 135°:

m∠1 + m∠2 = 135°

Substituting the given angle measures:

2x + (2x + 7) = 135

Combine like terms:

4x + 7 = 135

Subtract 7 from both sides:

4x = 128

Divide both sides by 4:

x = 32

Now we can find the measures of the two angles:

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

Therefore, m∠1 is 64° and m∠2 is 71°.