Question

If one angle of a parallelogram is of measure ${70}^{\circ }$, find the measures of all the angles of the parallelogram.

Answer 1

$LetparallelogrambePQRS$

$Let\angle P=70\left(given\right)$

$\angle R=70\left(oppositeanglesofparallelogramareequal\right)$

$\angle P+\angle Q=180\left(Interiorsidesonsamesideoftransversal\right)$

$\angle P=70$

$\angle Q+70=180$

$\angle Q=180-70$

$\angle Q=110$

$\angle Q=\angle S\left(oppositeanglesofparallelogramareequal\right)$

$\angle Qand\angle Sareequal$

$\angle S=110$

$\therefore anglesofparallelogramare\angle Q={110}^0,\angle R={70}^0,and\angle S={110}^0$