Question

In the given diagram, $XY\parallel PQ$. Find $x$ and $y$ respectively.

• A. ${75}^o$ and ${40}^o$
• B. ${45}^o$ and ${60}^o$
• C. ${75}^o$ and ${45}^o$
• D. ${60}^o$ and ${45}^o$

Answer 1

The correct option is A ${75}^o$ and ${40}^o$

$XY\parallel PQ$
So, $\angle EAY=\angle ABQ=60$
$\angle ABQ=\angle ABD+y=60$
$20+y=60$
$y=40$
$\angle YAB=180-60=120$
$\angle YAB=35+\angle DAB=120$
$\angle DAB=120-35=85$
IN triangle ADB
$\angle DAB+\angle x+\angle DBA=180$
$85+\angle x+20=180$
$\angle x=75$
Answer (A) ${75}^o$ and ${40}^o$