MathematicsIf the difference between two supplementary angles is 40°, then find the angles.

If the difference between two supplementary angles is 40°, then find the angles.

A
140 $°$ , 40 $°$
B
80 $°$ , 100 $°$
C
120 $°$ , 60 $°$
D
110 $°$ ,70 $°$

Solution:

Given that difference between two supplementary angles is 40°.
Supplementary angles means the angles whose sum is equal to 180

°

.
Let one of the angles be x, then another angle will be 180-x.
It is said that, the difference between these angles is 40

°

.
This implies,

x − (180 ° − x) = 40 ° ⇒ x + x − 180 ° = 40 ° ⇒ 2 x = 40 + 180 ⇒ 2 x = 220 ° ⇒ x = 220 ° 2 ⇒ x = 110 °

Other angle will be 180

°

- 110

°

= 70

°

So, the angles are 70

°

and 110

°

.
Therefore option 4 is correct.