The complement of an angle is one-eight the measure of the supplement of the angle. What is the measure of the supplement angle to the nearest hundredth of a degree?
Responses
A 102.86°102.86°
B 101.14°101.14°
C 105.17°105.17°
D 99.13°99.13°
E 103.05°103.05°
Let's call the angle x.
The complement of x is 90-x.
The supplement of x is 180-x.
According to the problem,
90-x = (1/8)*(180-x)
Multiplying both sides by 8 gives:
720-8x = 180-x
Simplifying:
7x = 540
x = 77.14
So the supplement of x is 180-x = 102.86, which is answer choice A.
To find the measure of the supplement angle, we'll first need to find the measure of the angle itself.
Let's call the angle x.
The complement of x is equal to 90° - x.
The supplement of x is equal to 180° - x.
According to the problem, the complement of x is one-eighth the measure of the supplement of x:
90° - x = (1/8)(180° - x)
To solve this equation, let's first distribute (1/8) to (180° - x):
90° - x = (1/8) * 180° - (1/8) * x
Simplifying the equation:
90° - x = 22.5° - (1/8) * x
Now, let's isolate the terms with x on one side of the equation:
x - (1/8) * x = 90° - 22.5°
Combining like terms:
(7/8) * x = 67.5°
Now, let's solve for x by isolating it:
x = (67.5° * 8) / 7
Simplifying:
x ≈ 77.14°
Now, let's find the measure of the supplement angle:
Supplement of x = 180° - x
Supplement of x ≈ 180° - 77.14°
Supplement of x ≈ 102.86°
Therefore, the measure of the supplement angle to the nearest hundredth of a degree is approximately 102.86°.
Answer: A) 102.86°
To solve this problem, we need to use the definitions of the complement and supplement of an angle.
The complement of an angle is the angle that, when added to the given angle, equals 90 degrees.
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
Let's say the measure of the angle is x degrees.
According to the problem, the complement of the angle is one-eighth the measure of the supplement of the angle. Mathematically, we can write this as:
90 - x = (1/8) * (180 - x)
To find the measure of the supplement angle, we need to solve this equation.
First, let's simplify the equation by multiplying both sides by 8 to eliminate the fraction:
8 * (90 - x) = 180 - x
Now, let's distribute the 8 on the left side of the equation:
720 - 8x = 180 - x
Next, let's combine like terms by adding 8x to both sides of the equation:
720 = 180 + 7x
Now, let's subtract 180 from both sides to isolate the term with x:
540 = 7x
Finally, let's solve for x by dividing both sides by 7:
x = 540/7 ≈ 77.14
So, the measure of the angle is approximately 77.14 degrees.
To find the measure of the supplement angle, we can substitute this value back into the equation:
180 - x = 180 - 77.14 ≈ 102.86
Therefore, the measure of the supplement angle to the nearest hundredth of a degree is approximately 102.86 degrees.
Hence, the correct answer is option A: 102.86°.