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= °
We know that the sum of ∠1 and ∠2 is equal to the resulting angle of 135°.
Thus, we can set up the equation:
∠1 + ∠2 = 135.
Substituting the given expressions for ∠1 and ∠2, we get:
(2x) + (2x + 7) = 135.
Combining like terms, we have:
4x + 7 = 135.
Subtracting 7 from both sides, we have:
4x = 128.
Finally, dividing both sides by 4, we find:
x = 32.
Therefore, the measure of ∠1 is:
∠1 = 2(32) = 64°
and the measure of ∠2 is:
∠2 = 2(32) + 7 = 71°.
So, m∠1 = 64° and m∠2 = 71°.