====== 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:**\\ {{ :matric:9th_science:unit11:ex11-1-9th-science-ptb-q-1.svg?nolink |Picture for Question 1}} 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:**\\ {{ :matric:9th_science:unit11:ex11-1-9th-science-ptb-q-2.svg?nolink |Picture for Question 2}} 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}