Question

the exterior angle of atriangle is 135° and one of the interior angle is 65°.find the other interior angle.​

Answer 1

$\huge\underline\mathrm{Question-}$

The exterior angle of atriangle is 135° and one of the interior angle is 65°. find the other interior angle.

$\huge\underline\mathrm{Answer-}$

Other two angles are of 45° and 70°

$\huge\underline\mathrm{Explanation-}$

Given :

$\angle{ACD}$ = 135°

$\angle{ABC}$ = 65°

To find :

• Other two interior angles of ∆ABC

Solution :

We know that, an exterior angle of a triangle is equal to the sum of its interior opposite angles.

$\therefore$ $\angle{ACD}$ = $\angle{ABC}$ + $\angle{BAC}$

★ Putting the given values,

: $\implies$ 135° = 65° + $\angle{BAC}$

: $\implies$ 135° - 65° = $\angle{BAC}$

: $\implies$ $\angle{BAC}$ = 70°

$\rule{200}2$

In ∆ABC, applying angle sum property,

$\angle{BAC}$ + $\angle{ABC}$ + $\angle{ACB}$ = 180°

: $\implies$ 70° + 65° + $\angle{ACB}$ = 180°

: $\implies$ 135° + $\angle{ACB}$ = 180°

: $\implies$ $\angle{ACB}$ = 180° - 135°

: $\implies$ $\angle{ACB}$ = 45°

$\therefore$ Other two angles are of 45° and 70°.

*Note : You can also find angle ACB by using linear pair property that states that sum of two angles on a straight line is of 180°.