Question

In the given figure (not drawn to scale), UT || SR and TR || SV, then find $\angle$a and $\angle$b.

• A. $a={115}^o,b={40}^o$
• B. $a={120}^o,b={65}^o$
• C. $a={145}^o,b={55}^o$
• D. $a={105}^o,b={35}^o$

Answer 1

The correct option is A $a={115}^o,b={40}^o$

In the given figure UT || SR and TR || SV,
Then $\angle$ UTR=$\angle$ PRQ=90 ${}^0$
In triangle PQR
$\angle$ RPQ+$\angle$ RQP+$\angle$ PRQ=180${}^0$
Then $\angle$ RQP(b)=180-90-50=40${}^0$
TR||SV
THen $\angle$ a=$\angle$ RTU+VUVS=90+25=115${}^0$