Question

A triangle has all the side lengths equal. Find the exterior angles.

• A. ${60}^o$
• B. ${90}^o$
• C. ${120}^o$
• D. ${150}^o$

Answer 1

The correct option is C ${120}^o$

The triangle which has equal side lengths is called an equilateral triangle.

Also, it can be proved that all the interior angles are equal in measure and are equal to ${60}^o.$

An equilateral triangle is a special type of isosceles triangle.

In an isosceles triangle, two angles have an equal measure, located opposite to the sides of equal length.

In an equilateral triangle, as all the sides have equal length, all the angles must have equal in measure.


Using interior angle property sum,
$\angle P+\angle Q+\angle R={180}^o$
$\Rightarrow 3\angle R={180}^o$
$\Rightarrow \angle R=\frac{{180}^o}{3}={60}^o$

Hence, $\angle P=\angle Q=\angle R={60}^o$

Now, exterior angle at R $={180}^o-{60}^o={120}^o$

$\therefore$ All the exterior angles are ${120}^o$ in measure.