Question

An exterior angle of a triangle measures 110 degree and it's interior opposite angles are in the ratio 2:3.Find of the angles of the triangle​.​

Answer 1

$\huge \tt \colorbox{lightpink}{Answer}$

Given the exterior angle of a triangle measure 110 degrees.

Given the interior angles are in the ratio 2x and 3x.

We know that sum of interior angles = 180.

           2x + 3x = 180

              5x = 180

                x = 36.

Then 2x = 72 and 3x = 108.

The angles are 36,72 and 108.

$\huge\purple{❥hope \: it \: helps}$

Answer 2

Answer :-

• The interior angles of triangle are 70°, 44° and 66°.

Step-by-step explanation :

To Find :-

• The angles of triangle

Solution :-

Given that,

• A exterior angle of triangle = 110°
• The two interior opposite angles of triangle are in the ratio of 2:3

Assumption: Let us assume the two opposite interior angles as ∠1 and ∠2, and the other unknown interior angle as ∠3

First we need to find out the other interior angle of triangle,

• (other interior angle) ∠3 + exterior angle = 180° .... [ linear pair ]

=> ∠3 + 110 = 180

=> ∠3 = 180 - 110

=> ∠3 = 70

Hence,

• The measure of other interior angle is 70°.

Now, we can find out the measure of each angle of triangle by " angle sum property of triangle ".

• 2x + 3x + 70° = 180°

=> 2x + 3x + 70 = 180

=> 2x + 3x = 180 - 70

=> 2x + 3x = 110

=> 5x = 110

=> x = 110/5

=> x = 22

• The value of x is 22.

Therefore, the angle are,

• The angle which we assumed as 2x [ ∠1 ]

=> 2x

=> 2*22

=> 44°

• The angle which we assumed as 3x [ ∠2 ]

=> 3x

=> 3*22

=> 66°

∴ The interior angles of triangle are 70°, 44° and 66°.