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.