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?
Since ∠1 and ∠2 are adjacent angles forming a resulting angle with measure 135°, we can write the equation:
∠1 + ∠2 = 135°
Substituting the given 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 unknown angle measures are:
∠1 = 2x = 2(32) = 64°
∠2 = 2x + 7 = 2(32) + 7 = 71°