Question

The sum of any two interior angles of a triangle is ${115}^o.$ Find the third angle.

• A. $5^o$
• B. ${60}^o$
• C. ${65}^o$

Answer 1

The correct option is C ${65}^o$

Let the three angles of a triangle be $\angle a,\angle b$ and $\angle c.$

We know that the sum of the angles of a triangle is ${180}^o.$
$\therefore \angle a+\angle b+\angle c={180}^o$

Given that sum of any two interior angle is ${115}^o.$
$\therefore$ Suppose $\angle a+\angle b={115}^o$
Substituting this in the above equation we get,
${115}^o+\angle c={180}^o$
$\Rightarrow \angle c={180}^o-{115}^o={65}^o$

$\therefore$ The third angle is ${65}^o.$