Question

In the given figure, PQ, RS and UT are parallel lines.

If $c={57}^o$ and $a=\frac{c}{3}$, then find the value of $d$.

• A. ${132}^o$
• B. ${136}^o$
• C. ${142}^o$
• D. ${146}^o$

Answer 1

The correct option is C ${142}^o$

Given , $c={57}^o$

$c=a+b={57}^o$........... (Alternating Opposite Angle).........(1)

$\Rightarrow \frac{c}{3}=a\Rightarrow c=3a\Rightarrow {57}^o=3a\Rightarrow a=\frac{{57}^o}{3}=19$

Putting this in (1)

$3a=a+b\Rightarrow b=2a=2\times 19=38$

Now, $b+d={180}^o$...........(Adjacent Angles are Supplementary)

$\Rightarrow d={180}^o-{38}^o$

$={142}^o$