Question

The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are ___________.

Answer 1

Let the two angles be x and y (x > y).

Supplement of angle x = 180º − x

Complement of angle y = 90º − y

Now,

180º − x + 90º − y = $\frac{1}{2}$ × 360º

⇒ 270º − x − y = 180º

⇒ x + y = 90º .....(1)

Also,

x = y + 10º

⇒ x − y = 10º .....(2)

Adding (1) and (2), we get

x + y + x − y = 90º + 10º

⇒ 2x = 100º

⇒ x = $\frac{100°}{2}$ = 50º

Substituting the value of x in (1), we get

50º + y = 90º

⇒ y = 90º − 50º = 40º

Thus, the measure of the angles are 40º and 50º.

The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are ___40º and 50º___.