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# Complementary angles and supplementary angles example

Question:

The complementary angle of an angle is equal to two-fifths of supplementary angle of this angle. find the degree measure of this angle.

Solution:

Let the degree measure of this angle be x.

The definition of complementary angles is: If angle1 plus angle2 equals 90o, then angle1 and angle2 are complementary angles.

The definition of supplementary angles is: If angle1 plus angle2 equals 180o, then angle1 and angle2 are supplementary angles.

The complementary angle of this angle is: 90 - x

The supplementary angle of this angle is: 180 - x

Their relation is: 90 - x = (2/5) (180 - x)

This is a one variable first degree equation, solve this equation,

90 - x = (2/5) (180 - x)
remove parentheses
90 - x = (2/5) 180 - (2/5) x
move all x term into left side of the equation, move all constant term into right side of the equation
(2/5) x - x = (2/5) 180 - 90
- (3/5) x = 2 × 36 - 90
- (3/5) x = 72 - 90
- (3/5) x = - 18
both side of the equation divide by - 3
x/5 = 6
x = 30

Therefore, the angle is 30o. Watch the video for more details.