# Exercise 11.1 (Solutions)

On this page solutions of Exercise of Unit 11: Parallelograms and Triangles of Mathematics 9 written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq has been given. There are two questions in this exercise and solution of both the questions are given below.

**Q.1 One angle of parallelogram is $130^\circ$. Find the measures of its remaining angles.**

**Solution:**

In a parallelogram $ABCD$, $m\angle B=130^\circ$

$m\angle B=m\angle D$ (Opposite angles of parallelogram)

$m\angle B=m\angle D=130^\circ$

We know that

\begin{align}
& m\angle A +\,\,m\angle B=180^\circ \\
& m\angle A+\,{{130}^{\circ }}={{180}^{\circ }}\\
& m\angle A={{180}^{\circ }}-{{130}^{\circ }}\\
& m\angle A={{50}^{\circ }}\end{align}
Also we have $m\angle A=m\angle C$ (Opposite angles of parallelogram)

$\Rightarrow \,\,\,\,m\angle C=50^\circ$

**Q.2 One exterior angle formed on producing one side of a parallelogram is $40^\circ$. Find the measures of its interior angles.**

**Solution:**

Given In a parallelogram $ABCD$, $m\angle DAM=40^\circ$

To find: $m\angle B=?$, $m\angle DAB=?$, $m\angle C=?$, $m\angle D=?$

\begin{align} & m\angle DAM+m\angle DAB=180^\circ \\ & 40^\circ + m\angle DAB= 180^\circ \\ & m\angle DAB=180^\circ- 40^\circ \\ & m\angle DAB=140^\circ \end{align} Also \begin{align} & m\angle DAB+m\angle B=180^\circ \\ & 140^\circ+m\angle B=180^\circ \\ & m\angle B=180^\circ-140^\circ \\ & m\angle B=40^\circ \end{align}

Now \begin{align} & m\angle B =m\angle D=40^\circ \\ \Rightarrow \,\,\,\,\,\,\,\,\, & m\angle D=40^\circ \end{align}

Also \begin{align} & m\angle C=m\angle DAB \\ \Rightarrow \,\,\,\,\,\,\,\,\, & m\angle C=140^\circ \end{align}