Question

4. If one of the angles of triangle is 65◦ and the other two angles are in the ratio of 2 : 3. Find the other two angles.

Answer 1

Given: One of the angles in a triangle measures 65° and the other two are in the ratio 2:3.

To find: The two angles.

Answer:

We know that all angles in a triangle add up to 180°.

Let the unknown 2 angles be 2x and 3x. (2:3)

65° + 2x +3x = 180°

65° + 5x = 180°

5x = 180° - 65°

5x = 115°

x = 115°/5

x = 23

Therefore, the other two angles are 2x =2*23 = 46° and 3x = 3*23 = 69°.

Hope it helps :)

Answer 2

Given, measure of one of the angles of a triangle is 65°

Given, the other two angles of the triangle are in the ratio 2 : 3

Let the 1st angle be 2x and 3rd angle be 3x


Three angles of a triangle add upto 180°


According to the question,

2x + 3x + 65 = 180

➾ 5x + 65 = 180

➾ 5x = 180 - 65

➾ 5x = 115

➾ x = $\dfrac{115}{5}$

➾ x = 23



∴ 1st angle ➾ 2x

➾ 2 × 23

➾ $\boxed{\boxed{\boxed{\boxed{46^{\circ}}}}}$



∴ 2nd angle ➾ 3x

➾ 3 × 23

➾ $\boxed{\boxed{\boxed{\boxed{69^{\circ}}}}}$