Question

In the adjacent figure $△ABC\sim △PQR$, and $\angle C={53}^{\circ }$. Find the side $PR$ and $\angle P$

Answer 1

$△ABC\sim △PQR$
When two triangles are similar their corresponding angles are equal and corresponding angles are equal and corresponding sides are in proportion.
$\frac{PR}{AC}=\frac{PQ}{AB}\Rightarrow \frac{PR}{5}=\frac{2}{4}$
$PR=\frac{2}{4}\times 5=2.5$
Again
$\angle R=\angle C={53}^{\circ }$
Sum of all three angles in a triangle as ${180}^{\circ }$
i.e. $\angle P+\angle Q+\angle R={180}^{\circ }$
$\angle P={90}^{\circ }+{53}^{\circ }={180}^{\circ }$
$\angle P={180}^{\circ }-{143}^{\circ }={37}^{\circ }$