Question

In the given figure $△ABC$ side $AC$ has been produced to $D$. $\angle BCD={125}^o$ and $\angle A:\angle B=2:3$, find the measure of $\angle A$ and $\angle B$.

Answer 1

Let $\angle A=2x$ and $\angle B=3x$

$\angle BCD=\angle B+\angle A$ (Sum of exterior angle of triangle is equal to sum of two opposite interior angles )

$2x+3x={125}^{\circ }5x={125}^{\circ }x=\frac{{125}^{\circ }}{5}={25}^{\circ }\angle A=2x=2\times {25}^{\circ }={50}^{\circ }\angle B=3\times {25}^{\circ }={75}^{\circ }$