Question

The angle and its supplement give the same quotient when divided by 7 and 13 respectively. Find the measure of the angle.

Solve this fast

Answer 1

Angle = X°                     Supplement = 180° - X°

For angle X° and 180 - X, let quotient be =  q°  and  remainder be = 0.
       X° = 7 * q

so  180 - X° =  180° - 7 q  = 13 * q° 
so   20 q = 180°

So q = 9°         and angle X = 63°

Answer 2

Let the Angle be α
Supplement = 180 - α
α / 7 = 180 - α / 13
13 × α = 7(180 - α)
13α = 1260 - 7α
13α + 7α = 1260
20α = 1260
α = 1260 / 20 = 63°
∴Angle = 63°
  Supplement = 180° - 63° = 117°
This Solution is Approved as:
63 / 7 = 9 
117 / 13 = 9.