In $ riangle PQR$, if $4\angle P = 5\angle Q = 20\angle R$, then the value of $\angle Q$ is:

Question

In $	riangle PQR$, if $4\angle P = 5\angle Q = 20\angle R$, then the value of $\angle Q$ is:

Accepted Answer

72°. Let $4P=5Q=20R=k$. Then $P=\frac{k}{4}$, $Q=\frac{k}{5}$, and $R=\frac{k}{20}$. Using $P+Q+R=180^\circ$, we get $\frac{k}{4}+\frac{k}{5}+\frac{k}{20}=180$, so $k=360$ and hence $Q=\frac{360}{5}=72^\circ$.

In $\triangle PQR$, if $4\angle P = 5\angle Q = 20\angle R$, then the value of $\angle Q$ is:

Solution

Related SSC CGL (Prelims) Maths questions