Question

If AB $\parallel$ CD, then find $\angle PCD$ and $\angle CPD$ from the adjoining figure

• A. $\angle PCD={44}^{\circ },\angle CPD={80}^{\circ }$
• B. $\angle PCD={68}^{\circ },\angle CPD={80}^{\circ }$
• C. $\angle PCD={28}^{\circ },\angle CPD={80}^{\circ }$
• D. $\angle PCD={71}^{\circ },\angle CPD={80}^{\circ }$

Answer 1

The correct option is A $\angle PCD={44}^{\circ },\angle CPD={80}^{\circ }$

$Given\angle APC={100}^o,\angle DAB={56}^{o}Fromthefigure,\angle APD={180}^o\left[Straightangle\right]-----\left(1\right)Now\angle APD=\angle APC+\angle CPD------\left(2\right)From\left(1\right)\&\left(2\right),\angle APC+\angle CPD={180}^o\Rightarrow \angle CPD={180}^o-{100}^o\Rightarrow \angle CPD={80}^{o}GivenAB\parallel CD\&ADbethetransversal\angle DAB=\angle ADC={56}^o\left[AlternateAngle\right]In△PCD,\angle CPD+\angle PCD+\angle PDC={180}^o\Rightarrow \angle PCD=180-80-56[\angle PDC=\angle ADC]\Rightarrow \angle PCD=180-136\Rightarrow \angle PCD={44}^o$