Question

The interior opposite angles of an exterior angle are in ratio 3:4 and the exterior angle is 140°. Find the three angles of the triangle.

Answer 1

Answer:

The Exterior angle = sum of interior opposite angles.

The interior angles are in the ratio 3:4, so,

the angles will be equal to 3k and 4k, respectively

140° = 3k + 4k = 7k

k = 140°/7 = 20°

So, the angles will be 3(20°) = 60°, and 4(20°) = 80°

Sum of all angles in a triangle = 180°

60° + 80° + Third angle = 180 °

Third angle= 180° - (60+80)° = 180° - 140° = 40°

Therefore, the angles are: 40°, 60°, 80°

Answer 2

Answer:

∠A = 60°

∠B = 80°

∠C = 40°

Step-by-step explanation:

Let ∠A, ∠B and ∠C are the three angles of a triangle.

Then ∠A + ∠B + ∠C = 180  ----------1     (By the property of triangle)

Let ∠D is the exterior angle.

So, ∠D = 140°    (Given)

Let ∠A and ∠B are the opposite interior angles. Then-

∠A + ∠B = ∠D            

(Because the sum of two opposite interior angles is equal to exterior angle.)

Given that-

∠A : ∠B = 3 : 4

Let ∠A = 3x

∠B = 4x

So, ∠A + ∠B = ∠D

3x + 4x = 140

7x = 140

$x = \dfrac{140}{7}$

x = 20

So, ∠A = 3x

            = 3×20

∠A = 60°

∠B = 4x

     = 4×20

∠B = 80°

From equation 1.

∠A + ∠B + ∠C = 180

60 + 80 + ∠C = 180

140 + ∠C = 180

∠C = 180 - 140

∠C = 40°

Hence, ∠A, ∠B and ∠C are 60°,  80° and 40°.