Question

One of the exterior angle of a triangle is 105º and the interior opposite angles are in the
ratio 2:5. Find the angles of the triangle.
​

Answer 1

Answer:

75° and 30° are the required angles

Step-by-step explanation:

let 5x and 2x be the required angles

now, 2x+5x=105(exterior angles property of triangle)

7x=105

x=105/7

x=15

now, 5x 15=75

2x 15=30

Answer 2

Given:

• exterior angle of the triangle = 105°
• ratio of the interior angles of the triangle = 2:5

To Find:

angles of the triangle

Solution:

We Know That:

${ \boxed { \sf{ \purple{\: exterior \: angle \: is \: equal \: to \: sum \: of \: all \: interior \: angle}}}}$

it is given that,

interior angles of the exterior angle 105° are in ratio 2:5

therefore,

$\sf{\:2x + 5x = 105 \degree}$

$\implies\sf{7x = 105 \degree }$

$\implies\sf{x = \frac{7}{105}}$

$\implies\sf\underline\red{ x = 15 \degree}$

now, interior angles of the exterior angle 105° are:

$\implies\sf{ 2x = 2 \times 15}$

$\implies\sf\underline\purple{2x = 30 \degree}$

$\implies\sf{ 3x = 3 \times 15}$

$\implies\sf\underline\purple{3x = 75 \degree}$

Now,let the third angle be "y"

We Know That:

${\boxed{\sf{\orange{sum\:of\:all\: interior\:angles\:of\: triangle\:is\:180 \degree}}}}$

therefore,

$\implies\sf{30 \degree + 75 \degree + y = 105 \degree}$

$\implies\sf{y = 180 \degree - 105 \degree}$

$\implies\sf\underline\pink{y = 75 \degree}$

Hence,

the measure of the interior angles of the triangle are 30°,75° and 75°