Two adjacent angles, ∠1 and ∠2, form a resulting angle with measure 135°. The measure of ∠1 is (2x)° and the measure of ∠2 is (2x+7)°. What are the two unknown angle measures?
Since ∠1 and ∠2 are adjacent angles, their measures add up to the measure of the resulting angle. Therefore, we have the equation (2x)° + (2x+7)° = 135°.
Combining like terms, we have 4x + 7 = 135.
Subtracting 7 from both sides, we isolate 4x and have 4x = 128.
Dividing both sides by 4, we find x = 32.
Plugging this value back into the expressions for ∠1 and ∠2, we find that ∠1 measures (2*32)° = 64°, and ∠2 measures (2*32+7)° = 71°.