Question:
Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.
Solution:
We know that the adjacent angle $s$ of a parallelogram are supplementry.
Hence, $(3 x+10)^{\circ}$ and $(3 x-4)^{\circ}$ are supplementry.
$(3 x+10)^{\circ}+(3 x-4)^{\circ}=180^{\circ}$
$6 x^{\circ}+6^{\circ}=180^{\circ}$
$6 x^{\circ}=174^{\circ}$
$x=29^{\circ}$
First angle $=(3 \mathrm{x}+10)^{\circ}=\left(3 \times 29^{\circ}+10^{\circ}\right)=97^{\circ}$
Second angle $=(3 \mathrm{x}-4)^{\circ}=83^{\circ}$
Thus, the angles of the parallelogram are $97^{\circ}, 83^{\circ}, 97^{\circ}$ and $83^{\circ}$.