Question

For a triangle, all the angles are equal in measure. The measure of each angle is degree.

Answer 1

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 ${180}^o.$
$\therefore \angle a+\angle b+\angle c={180}^o$

Also, it is given that all the angles are equal in measure.
$\therefore \angle a=\angle b=\angle c$
Substituting this in the above equation we get,
$\angle a+\angle a+\angle a={180}^o$
$\Rightarrow 3\angle a={180}^o$
$\Rightarrow \angle a=\frac{{180}^o}{3}={60}^o$

$\therefore$ Measure of each angle is 60^o.$
It is an equilateral triangle.