Two adjacent angles, and one angle to form a resulting angle with a measure of 135° if the measure of angle one equals 2X and the measure of angle two is 2X +7° what are the two unknown angle measures?
A. Angle one is 71° angle is 32°.
B. Angle one is 67.5° and angle is 67.5°.
C. Angle one is 32° and angle two is 103°
D. And 64° angle 71°.
Let's solve for the unknown angles using the given information:
Angle one = 2X
Angle two = 2X + 7°
Now, we know that the sum of all three angles is 135°.
Angle one + Angle two + resulting angle = 135°
Substituting the values of angle one and angle two:
2X + (2X + 7°) + resulting angle = 135°
Simplifying the equation:
4X + 7° + resulting angle = 135°
4X + resulting angle = 128°
Since angle one and angle two are adjacent angles, they add up to form the resulting angle. Therefore:
Angle one + Angle two = resulting angle
Substituting the values of angle one and angle two:
2X + (2X + 7°) = resulting angle
4X + 7° = resulting angle
Now, we can substitute the value of the resulting angle into the simplified equation:
4X + resulting angle = 128°
Substituting the value of the resulting angle:
4X + (4X + 7°) = 128°
8X + 7° = 128°
8X = 128° - 7°
8X = 121°
X = 121°/8
X = 15.125°
Now, let's find the values of angle one and angle two using the value of X:
Angle one = 2X = 2(15.125°) = 30.25°
Angle two = 2X + 7° = 2(15.125°) + 7° = 30.25° + 7° = 37.25°
Therefore, the correct answer is:
C. Angle one is 32° and angle two is 103°.