Subjects geometry

Parallelogram Angles 1D17A6

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1. **State the problem:** We are given a parallelogram with sides and angles labeled, and we need to find the values of $x$, $m\angle ADB$, and $m\angle A$. 2. **Use properties of parallelograms:** Opposite sides are equal, and opposite angles are equal. Adjacent angles are supplementary (sum to 180°). 3. **Find $x$:** Given side $AD = 6x$ and side $BC = 18$. Since $AD$ and $BC$ are opposite sides, they are equal: $$6x = 18$$ Divide both sides by 6: $$\cancel{6}x = \frac{18}{\cancel{6}}$$ $$x = 3$$ 4. **Find $m\angle ADB$:** Given as 63° in the figure, so $$m\angle ADB = 63^\circ$$ 5. **Find $m\angle A$:** Given as 80° in the figure, so $$m\angle A = 80^\circ$$ **Final answers:** $$x = 3$$ $$m\angle ADB = 63^\circ$$ $$m\angle A = 80^\circ$$