**Question:**

The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.

**Solution:**

Let the angles be A, B, C and D.

It is given that the sum of two opposite angles is $130^{\circ}$.

$\therefore \angle \mathrm{A}+\angle \mathrm{C}=130^{\circ}$

$\angle \mathrm{A}+\angle \mathrm{A}=130^{\circ}$ (opp o site angle $s$ of a parallelogram are same)

$\angle \mathrm{A}=65^{\circ}$

and $\angle \mathrm{C}=65^{\circ}$

The s um of adjacent angles of a paralle $\log$ ram is $180^{\circ}$.

$\angle \mathrm{A}+\angle \mathrm{B}=180^{\circ}$

$65^{\circ}+\angle \mathrm{B}=180^{\circ}$

$\angle \mathrm{B}=180^{\circ}-65^{\circ}$

$\angle \mathrm{B}=115^{\circ}$

$\angle \mathrm{D}=115^{\circ}$

$\therefore \angle \mathrm{A}=65^{\circ}, \mathrm{v} \angle \mathrm{B}=115^{\circ}, \angle \mathrm{C}=65^{\circ}$ and $\angle \mathrm{D}=115^{\circ}$.