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:

Angle 1: 70

Angle 2: 80

Step-by-step explanation:

Let the common ratio be:x

Angle 1: 3x

Angle 2: 4x

Exterior angle= sum of 2 opposite interior angles.

.

. . 140°= 3x + 4x

140°= 7x

140/7=x

.

. . x= 20

Now,

Angle 1: 3×x= 3×20

3x=60

Angle 2: 4×x = 4×20

4x= 80.

Answer 2

We know,

$\sf An \: \: exterior \: \: \angle \: \: of \: \: a \: \: \triangle \: \: is \: \: sum \: \: of \\ \sf its \: \: opposite \: \: interior \: \: \angle s \: .$

Now,

$\implies3x + 4x = 140 \degree \\ \implies \: \: \: \: \: \: \: \: \: \: 7x = 140\degree \\ \implies \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{140\degree}{7} = 20\degree$

Hence,

$\bf \: {1}^{st} \: \angle \: \: of \: \triangle \: = \red{60\degree} \\ \bf {2}^{nd} \: \angle \: \: of \: \triangle \: = \red{80\degree} \\ \bf \: {3}^{rd} \: \angle \: \: of \: \triangle = \red{40\degree}$