Question

Two angles of a triangle are in the ration of 2:3.If the sum of these two angles is 30 degree less than the third angle,Find all the three angles?

Answer 1

SOLUTION:-

Let the third angle be y°.

Let the common multiple be x in 2:3

•°• 2x :3x

According to the Condition:-

If the sum of these two angles is 30 degree less than the third angle.

=> 2x + 3x = y - 30

•°• 5x - y = -30 .......1

sum of all angles is 180° of triangle:-

2x + 3x + y = 180

5x + y = 180 .......2

Adding eq1 and eq2 :-

5x - y = -30

+ 5x + y = 180

10x = 150

x = 150/10

x = 15

substituting x = 15 in eq1 :-

(5× 15) - y = -30

75 - y = -30

75 + 30 = y

105 = y

All angles:-

2x = 2× 15 = 30°

3x = 3× 15 = 45°

y = 105°

All three angles are 30°,45° and 105°.