Question

The sum of two angles of a triangle is equal to the third angle. If these two angles are in the ratio $4:5$, then find the value of each angle.

Answer 1

Let the given two angles are $4xand5x$.

According to the question, third angle is $4x+5x=9x$

We know that sum of all angles are ${180}^{°}$

i.e. $\angle A+\angle B+\angle C={180}^0$

So,

$$\begin{gathered} 4x+5x+9x=180 \\ 18x=180 \\ x=\frac{180}{18} \\ x=10 \end{gathered}$$

Hence, ∠A = $4\times 10={40}^{°}$ , ∠B = $5\times 10={50}^{°}$ and ∠C = $9\times 10={90}^{°}$.