Question

$ABCD$ is a rectangle. If $\angle BPC={124}^o$.
Calculate:
(i) $\angle BAP$
(ii) $\angle ADP$.

Answer 1

In $\Delta BPC$ and $\Delta APD$, it is known that the vertically opposite angles are equal, so,

$\angle BPC=\angle APD$

$\angle APD={124}^{\circ }$

In $\Delta APD$, the opposite angles are equal,

$\angle DAP=\angle ADP$

$\angle DAP+\angle ADP+\angle APD={180}^{\circ }$

$\angle ADP+\angle ADP={180}^{\circ }-{124}^{\circ }$

$\angle ADP={28}^{\circ }$

In rectangle ABCD,

$\angle DAB=\angle DAP+\angle PAB$

${90}^{\circ }={28}^{\circ }+\angle PAB$

$\angle PAB={62}^{\circ }$