T w o a d j a c e n t angles angle 1 and angle 2 form a resulting angle with a measure of 135° of the measure of an angle 1 equals two times degrees and the measure angle two is two times plus 7°, what are they two unknown angles measures a angle 1 is 71° and angle 2 is 32° B angle 1 is 67.5 and angle 2 is 67.5 degrees c angle 1 is 32 degrees and angle 2 is 103 degrees and angle 2 is 71°
To solve this problem, we can create an equation based on the given information.
Let x be the measure of angle 1.
According to the given information, angle 1 has a measure of 2 times x, which can be expressed as 2x.
Angle 2 has a measure of 2 times the measure of angle 1 plus 7 degrees, which can be expressed as 2(2x) + 7.
The resulting angle formed by angle 1 and angle 2 has a measure of 135 degrees.
Thus, we can set up the equation:
x + 2(2x) + 7 = 135
Simplifying, we get:
x + 4x + 7 = 135
5x + 7 = 135
5x = 135 - 7
5x = 128
x = 128/5
x = 25.6
Therefore, the measure of angle 1 is 25.6 degrees.
To find the measure of angle 2, we substitute the value of x back into the expression for angle 2:
2(2x) + 7
2(2(25.6)) + 7
2(51.2) + 7
102.4 + 7
109.4
Therefore, the measure of angle 2 is 109.4 degrees.
Therefore, the two unknown angle measures are:
Angle 1 is 25.6 degrees.
Angle 2 is 109.4 degrees.
None of the answer choices given match the correct solution.