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 adjacent angles form a resulting angle of 135°, we can set up the equation:
m∠1 + m∠2 = 135
2x + (2x + 7) = 135
4x + 7 = 135
4x = 128
x = 32
So the measure of ∠1 is:
m∠1 = 2x° = 2(32)° = 64°
And the measure of ∠2 is:
m∠2 = (2x + 7)° = (2(32) + 7)° = 71°
Therefore, the unknown angle measures are:
m∠1 = 64°
m∠2 = 71°