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= °
Since ∠1 and ∠2 are adjacent angles, their measures will add up to the measure of the resulting angle.
Therefore, we can set up the equation: ∠1 + ∠2 = 135°
Substituting in the given measures, 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
Now we can substitute this value back into the expressions for ∠1 and ∠2 to find their measures:
∠1 = 2x = 2(32) = 64°
∠2 = 2x+7 = 2(32)+7 = 71°
Therefore, the two unknown angle measures are: ∠1 = 64° and ∠2 = 71°.