Question

Two angles of a triangle are equal and the third angle is greater than each one of them by 18°. Find the angles.

Answer 1

Let $\angle A=\angle B\text{and}\angle C=\angle A+18°$.
Then,
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \angle A+\angle A+\angle A+18°=180° \\ \Rightarrow 3\angle A=162° \\ \Rightarrow \angle A=54° \end{gathered}$$
Since,
$$\begin{gathered} \angle A=\angle B \\ \Rightarrow \angle B=54° \\ \therefore \angle C=\angle A+18° \end{gathered}$$

$$\begin{gathered} =\left(54+18\right)° \\ =72° \end{gathered}$$