Question

one of the angles of a triangle is 65 degree and the other two acute angles are in ratio 2 :
3 find the other two angles​

Answer 1

Step-by-step explanation:

let the ratio be in X

2x : 3x

65 + 2x + 3x = 180 (angle sum property of triangle)

65 + 5x = 180

5x = 180 - 65

5x = 115

X = 115/5

x = 23

2nd angle = 2 × 23

= 46

3rd angle = 3 × 23

= 69

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Answer 2

Solution:

Let, 1st angle = ∠A

2nd angle = ∠B

3rd angle = ∠C

Given:

=> ∠A = 65°

=> ∠B : ∠C = 2:3

To find:

=> ∠B and ∠C

So,

Let ∠B and ∠C be 2x and 3x.

According to angle sum property, the sum of three angles of triangle is 180°

So,

=> ∠A + ∠B + ∠C = 180°

=> 65° + 2x + 3x = 180°

=> 5x = 180° - 65°

=> 5x = 115°

=> x = 115°/5

=> x = 23°

So, ∠A = 65°

∠B = 2x = 2 × 23° = 46°

∠C = 3x = 3 × 23° = 69°

Verification:

=> ∠A + ∠B + ∠C = 180°

=> 65° + 46° + 69° = 180°

=> 180° = 180°