Question

measure of the angles of the triangle MNP are in the ratio 2:3:5 find the measures of each angle and find the greatest angle​

Answer 1

Answer:

The greatest angle is 90° and the angles are :- ∠M = 36° ; ∠N = 54° and ∠P = 90°

solution:

Let the ratio angles of a triangle be 2x , 3x and 5x

The value of x is

⟹ 2x + 3x + 5x = 180°

⟹ 5x + 5x = 180 .........( The sum of triangle is 180°)

⟹ 10x = 180

⟹ x = 180/10

⟹ x = 18

Now, the angles are:-

• 2x ( ∠M )

⟹ 2 × 18

⟹ 36°

• 3x ( ∠N )

⟹ 3 × 18

⟹ 54°

• 5x ( ∠P )

⟹ 5 × 18

⟹ 90°

Now, Verification

⟹ ∠M + ∠N + ∠P = 180°

⟹ 36° + 54° + 90° = 180°

⟹ 90 + 90 = 180

⟹ 180 = 180

L.H.S = R.H.S

Hence, Proved.

Finally, The greatest angles are:-

The angles are:-

∠M = 36° ; ∠N = 54° and ∠P = 90°

90 54 36

So, the greatest angle is 90°