Question

7. One of the exterior angles of a triangle is 80° and the interior opposite angles are
in the ratio 5:3. Find the angles of the triangle.
PTV​

Answer 1

Answer:

$exterior \: angle = sum \: of \: oppostite \: interior \: angles$

$80° = 5x + 3x$

$8x = 80°$

$x = 10°$

$1st \: angle = 5x = 50°$

$2nd \: angle = 3x = 30°$

Answer 2

Given:-

• One of the exterior angles of a traingle is 80°
• The ratio of opposite angles of the interior traingle is 5 : 3

To Find:-

• Find the angles of triangle.

Solution:-

Given,

One of the exterior angles of a triangle is 80°

Let the angle B be " 5x "

The angle C be " 3x "

$\tt\implies \: 5x + 3x = 80$

$\tt\implies \: 8x = 80$

$\tt\implies \: x = \dfrac{80}{8}$

$\tt\implies \: x = 10$

$\tt \: \angle \: B =$

$\tt\implies \: 5x$

$\tt\implies \: 5(10)$

$\tt\implies \: {50}^{\circ}$

$\tt \: \angle \: C =$

$\tt\implies \: 3x$

$\tt\implies \: 3(10)$

$\tt\implies \: {30}^{\circ}$

We know that,

$\tt\implies \: \angle \: A + \angle \: B + \angle \: C = {180}^{ \circ }$

$\tt\implies \: \angle \: A + 30 + 50 = {180}^{\circ}$

$\tt\implies \: \angle \: A + 80 = {180}^{\circ}$

$\tt\implies \: \angle \: A = 180 - 80$

$\tt\implies \: \angle \: A = {100}^{\circ}$