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.
To solve this problem, we need to set up an equation and solve for x.
Since an obtuse angle is formed when the sum of two angles is greater than 90 degrees but less than 180 degrees, we can set up the following inequality:
(x + 10)° + (3x)° > 90°
Simplifying this inequality, we get:
4x + 10 > 90
Subtracting 10 from both sides, we get:
4x > 80
Dividing both sides by 4, we get:
x > 20
So the value of x must be greater than 20. Now we need to find the angle measures of each of the two unknown angles. We can substitute the value of x into the expressions for the angles:
First angle: x + 10 = 20 + 10 = 30 degrees
Second angle: 3x = 3 * 20 = 60 degrees
So the angle measures of the two unknown angles are approximately 30 degrees and 60 degrees, rounded to the nearest whole number.