Question

One angle of a triangle is ${40}^{\circ }$ and the other two angles have equal measures. Measure of each equal angle will be degree.

Answer 1

Let's name the vertices of triangle as A, B and C.
$m\angle A={40}^{\circ }m\angle B=m\angle C$

$\because m\angle A+m\angle B+m\angle C={180}^{\circ }\Rightarrow m\angle B+m\angle C={180}^{\circ }-\left(m\angle A\right)$
$\because m\angle B=m\angle C$
$\Rightarrow 2\left(m\angle B\right)={180}^{\circ }-{40}^{\circ }$
$\Rightarrow m\angle B=\frac{{180}^{\circ }-{40}^{\circ }}{2}=\frac{{140}^{\circ }}{2}={70}^{\circ }\Rightarrow m\angle C={70}^{\circ }$

Hence, the measure of the other two equal angles will be ${70}^{\circ }$