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
Since the two angles are adjacent, they share a common vertex and a common side. Therefore, the sum of the measures of the two angles will be equal to the measure of the resulting angle.
Let's call the measure of angle 1 (m<1) is 2x, and the measure of angle 2 (m<2) is 2x+7.
So, according to the problem, we need to solve the equation:
2x + (2x+7) = 135
Simplifying the equation:
4x + 7 = 135
4x = 135 - 7
4x = 128
x = 128/4
x = 32
Now, we can substitute the value of x back into the expressions for the angle measures:
m<1 = 2x = 2(32) = 64 degrees
m<2 = 2x+7 = 2(32)+7 = 64+7 = 71 degrees
Therefore, the measure of angle 1 is 64 degrees, and the measure of angle 2 is 71 degrees.