Question

In the given figure, $\square$PQRS and $\square$ABCR are two parallelograms. If $\angle$P = ${110}^{°}$ then find the measures of all angles of $\square$ABCR.

Answer 1

In $\square$PQRS,
$\angle$P = ${110}^{°}$
We know that opposite angles of a parallelogram are congruent.
So, $\angle$P = $\angle$R = ${110}^{°}$
In $\square$ABCR,
$\angle$R =$\angle$B = ${110}^{°}$ (Opposite angles of a parallelogram are congruent)
Interior angles on the same side of the transversal are supplementary.
So,
$$\begin{gathered} \angle \mathrm{R}+\angle \mathrm{A}=180° \\ \Rightarrow 110°+\angle \mathrm{A}=180° \\ \Rightarrow \angle \mathrm{A}=180°-110° \\ \Rightarrow \angle \mathrm{A}=70° \end{gathered}$$
And $\angle$A =$\angle$C = 110$°$.