Find the measure of an angle if its measure is 26° more than three times its complement.
(1 point)
Responses
16°
141°
74°
42°
Let x be the measure of the angle. The complement of the angle is (90 - x)°. According to the given information, 26° more than three times the complement is equal to the angle, so we can write the equation:
(90 - x) + 26 = 3(90 - x)
90 - x + 26 = 270 - 3x
26 = 270 - 2x
2x = 270 - 26
2x = 244
x = 244/2
x = 122
Therefore, the measure of the angle is 122°.
Let's start by setting up an equation to represent the problem.
Let the measure of the angle be x.
The complement of the angle is 90 - x.
According to the problem, the angle measure is 26 more than three times its complement, so we can write the equation as:
x = 3(90 - x) + 26
Simplifying the equation, we get:
x = 270 - 3x + 26
x + 3x = 270 + 26
4x = 296
x = 74
Therefore, the measure of the angle is 74°.
Hence, the correct answer is:
74°