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?
If we add the measures of ∠1 and ∠2, we get:
m∠1 + m∠2 = (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 = 32.
Now we can substitute this value back into the expressions for ∠1 and ∠2 to find their measures:
m∠1 = (2(32))° = 64°.
m∠2 = (2(32) + 7)° = 71°.
Therefore, the two unknown angle measures are 64° and 71°.