An obtuse angle is formed by two adjacent angles with measures (x + 10)° and (3x)° . If the resulting angle measure is 118° , what is the angle measure of each of the two unknown angles? Round to the nearest whole number.
A. 43° and 75°
B. 37° and 81°
C. 20° and 98°
D. 34° and 84°
The sum of two adjacent angles is equal to the measure of the obtuse angle:
(x + 10)° + (3x)° = 118°
Combine like terms:
4x + 10 = 118
Subtract 10 from both sides:
4x = 108
Divide both sides by 4:
x = 27
Now we can find the measure of each angle:
First angle: (x + 10)° = 27 + 10 = 37°
Second angle: (3x)° = 3(27) = 81°
Therefore, the measure of each of the two unknown angles is 37° and 81°, so the answer is B. 37° and 81°.