Question

An exterior angle of a triangle is $110°$, and one of the interior opposite angle is $30°$. Find the other two angles of the triangle.

• A. $80°$ and $20°$
• B. $70°$ and $40°$
• C. $20°$ and $70°$
• D. $80°$ and $70°$

Answer 1

The correct option is D

$80°$ and $70°$

Explanation for the correct option:

Find the other two angles of the triangle.

It is known that, an exterior angle of a triangle is equal to the sum of interior opposite angles of the triangle.

So, $30°$ $+$ other interior angle $=110°$

Thus, the other interior angle $=110°-30°=80°$

By the angle sum property of a triangle,

$30°$ $+$ $80°$ $+$ third angle $=180°$

Thus, the third angle $=180°-80°-30°=70°$

Hence, the angles are $80°$ and $70°$.

Hence, option (D) is correct answer.