An obtuse angle is formed by two adjacent angles with measures (x - 5) degrees and (3x) degrees. If the resulting angle measure is 107 degrees, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.

Question

A. 23 degrees and 84 degrees
B. 32 degrees and 75 degrees
C. 28 degrees and 79 degrees
D. 20 degrees and 87 degrees

Answer 1

First, we need to set up an equation using the information given:

(x - 5) + (3x) = 107

Combining like terms:

4x - 5 = 107

Adding 5 to both sides:

4x = 112

Dividing by 4:

x = 28

Now, we can find the measures of the two unknown angles:

First angle: x - 5 = 28 - 5 = 23 degrees
Second angle: 3x = 3(28) = 84 degrees

Therefore, the angle measures of the two unknown angles are 23 degrees and 84 degrees. Rounding to the nearest whole number, the answer is A. 23 degrees and 84 degrees.