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?
Given that ∠1 = (2x)° and ∠2 = (2x + 7)°, we can set up the equation:
∠1 + ∠2 = 135°
Plug in the values:
(2x)° + (2x + 7)° = 135°
Combine like terms:
4x + 7 = 135
Subtract 7 from both sides:
4x = 128
Divide both sides by 4:
x = 32
Now we can find the unknown angle measures:
∠1 = (2x)° = (2 * 32)° = 64°
∠2 = (2x + 7)° = (2 * 32 + 7)° = 71°
Therefore, the two unknown angle measures are 64° and 71°.