Two adjacent angles, ∠1 and ∠2, form a resulting angle that measures 135° . If m∠1 = (2x)° and m∠2 = (2x + 7)° , what are the two unknown angle measures?

Answer 1

Since ∠1 and ∠2 are adjacent angles, their measures add up to the measure of the resulting angle.
So m∠1 + m∠2 = 135°.
Substituting the expressions for m∠1 and m∠2, 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 get x = 128/4 = 32.
Therefore, m∠1 = (2x)° = (2*32)° = 64°.
And m∠2 = (2x + 7)° = (2*32 + 7)° = 71°.
So the unknown angle measures are 64° and 71°.