Question

Two adjacent angle of $||gm$ are $2x-{15}^o$ and $7x-{75}^o$.Find all angles of $||gm$ ?

Answer 1

Adjacent angles of a parallelogram add up to ${180}^o$, using that:
$2x-{15}^o+7x-{75}^o={180}^o⟹9x-{90}^o={180}^o$
$⟹9x={270}^o⟹x={30}^o$
Therefore, the angles are $2x-{15}^o=2\cdot {30}^o-{15}^o={45}^o$
Other ange = ${180}^o-{45}^o={135}^o$
As opposite angles of a parallelogram are equal, the other two angles are also ${45}^o$ and ${135}^o$.