1. **State the problem:** We have a parallelogram with an interior angle $a = 48^\circ$. We want to find the values of $a$ and $b$. 2. **Recall properties of a parallelogram:** - Opposite angles are equal. - Adjacent angles are supplementary, meaning they add up to $180^\circ$. 3. **Given:** - Angle $a = 48^\circ$ (one interior angle). 4. **Find angle $b$:** Since $a$ and $b$ are adjacent angles in a parallelogram, they satisfy: $$a + b = 180^\circ$$ Substitute $a = 48^\circ$: $$48^\circ + b = 180^\circ$$ 5. **Solve for $b$:** $$b = 180^\circ - 48^\circ$$ $$b = 132^\circ$$ 6. **Summary:** - $a = 48^\circ$ because it is given. - $b = 132^\circ$ because adjacent angles in a parallelogram sum to $180^\circ$. **Final answers:** $$a = 48^\circ$$ $$b = 132^\circ$$