The acute angle is (2x)° and the obtuse angle is (5x - 22)° . what is the simplified equation corresponding to the measures of the angles
A. (7x - 22)° = 180°
B. (3x - 22)° = 180°
C. (3x - 22)° = 90°
D. (7x - 22)° = 90°
The sum of the measures of an acute angle and an obtuse angle is always equal to 180°. Therefore, we can write the equation as follows:
(2x)° + (5x - 22)° = 180°
Combining like terms, we have:
7x - 22° = 180°
Adding 22° to both sides, we get:
7x = 202°
Dividing both sides by 7, we have:
x = 29°
So, the correct answer is:
(7x - 22)° = 90°
Therefore, the simplified equation corresponding to the measures of the angles is option D.