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, the measure of the angle is 26° more than three times its complement.
This can be expressed as: x = 3(90° - x) + 26.
Simplifying the equation, we get:
x = 270° - 3x + 26°.
Combining like terms:
4x = 296°.
Dividing both sides by 4:
x = 74°.
Therefore, the measure of the angle is 74°.
The correct answer is:
74°
Let's call the measure of the angle x. The complement of an angle is the angle that, when added to the given angle, adds up to 90° (since the sum of an angle and its complement is 90°).
The complement of x is therefore 90° - x.
The problem states that the measure of the angle is 26° more than three times its complement, which can be written as:
x = 3(90° - x) + 26
Let's solve this equation to find the value of x.
x = 3(90° - x) + 26
x = 270° - 3x + 26
4x = 270° + 26
4x = 296°
x = 296° / 4
x = 74°
So, the measure of the angle is 74°.
Therefore, the answer is 74°.