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=
°
m∠1 = 2x
m∠2 = 2x + 7
Since the two angles are adjacent, their sum should be equal to the resulting angle measure:
m∠1 + m∠2 = 135°
Substituting the given values:
2x + (2x + 7) = 135
Combining like terms:
4x + 7 = 135
Subtracting 7 from both sides:
4x = 128
Dividing both sides by 4:
x = 32
Now we can find the values of m∠1 and m∠2:
m∠1 = 2x = 2(32) = 64°
m∠2 = 2x + 7 = 2(32) + 7 = 71°
Therefore, the unknown angle measures are:
m∠1 = 64°
m∠2 = 71°