Question

The measures of angles of a, $\square$PQRS are 3x, 4x, 5x and 6x repeatively find x and the measures of $\angle$P ,$\angle$Q, $\angle$R and $\angle$S.

Answer 1

By the angle addition property of a quadrilateral, we have:

$\angle \mathrm{P}+\angle \mathrm{Q}+\angle \mathrm{R}+\angle \mathrm{S}=360°$
We know,
$$\begin{gathered} \angle \mathrm{P}=3x,\angle \mathrm{Q}=4x,\angle \mathrm{R}=5x\mathrm{and}\angle \mathrm{S}=6x \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ 3x+4x+5x+6x=360° \\ \Rightarrow 18x=360° \\ \Rightarrow x=20° \\ \mathrm{Thus},\mathrm{the}\mathrm{measures}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{quadrilateral}\mathrm{PQRS}\mathrm{are}: \\ \angle \mathrm{P}=3\times 20°=60° \\ \angle \mathrm{Q}=4\times 20°=80°, \\ \angle \mathrm{R}=5\times 20°=100° \\ \angle \mathrm{S}=6\times 20°=120° \end{gathered}$$