Angles Relationship (Angles Word Problems)

Few problems about angles relationship are given in a word problems.

Problem 1.
The complement of an angle is 56º. What is the measure of the angle?
Solution:

Assumed: The angle is x, then its complement is 90º - x.

The mathematics model of "The complement of an angle is 56º" is:

90º - x = 56º
-x = 56º - 90ºº
-x = -34º
x = 34ºº

Then the measure of the angle is 34º.

Problem 2.
The magnitude of an angle is 5 times of its supplement. What is the magnitude of the angle?
Solution:
Assumed: The angle is x, then its supplement is 180º - x.

The mathematics model of "The magnitude of an angle is 5 times of its supplement" is:

x = 5(180º - x)
x = 900º - 5x
x + 5x = 900º
6x = 900º
x = 150º

Then the magnitude of the angle is 150º.

Problem 3.
The complement of an angle is a quarter of the supplement of the angle. What is the 5 times of the angle?

Solution:

Assumed the angles is x, then

the complement is 90º - x and

its supplement is 180º - x.

The mathematics model of "The complement of an angle is a quarter of the supplement of the angle" is:

(90º - x) = 1/4 (180º - x)
4(90º - x) = 180º - x
360º - 4x = 180º - x
-4x + x = 180º - 360º
-3x = -270º
3x = 270º
x = 90º

Then 5 times of the angle = 5.90º = 450º.

Problem 4.
The supplement of twice (2 times) of the complement of an angle is 80º. What is 1/4 of the angle?

Solution:

Assume: angle = x
The complement = 90º - x
2 times of the complement = 2 (90º – x)
Supplement of 2 times of the complement = 180º - 2 (90º - x) = 80º

180º - 2 (90º - x) = 80º

180º - 180º + 2x = 80º

2x = 80º

x = 40º

Therefore 1/4 of the angle = 1/4 . 40º = 10º

Problem 5.

The complement of 1/2 supplement of 1/4 of an angle is 20º. Determine the magnitude of the angle!

Solution:
Assume: angle = x
1/4 of angle = 1/4 x
supplement of 1/4 of angle = 180º - 1/4 x
1/2 supplement 1/4 of angle = 1/2 (180º - 1/4 x)
complement of 1/2 of supplement of 1/4 angle:

90º - 1/2 (180º - 1/4 x) = 20º (open the brackets)
90º - 90º + 1/8 x = 20º
1/8 x = 20º
x = 160º

Therefore the magnitude of the angle is 160º.