Question

In figure, given that $AB\parallel CD$. If $\angle 1=(120-x^o)$ and $\angle 5=5x^o$, find the measures of $\angle 1$ and $\angle 5$.

• A. $\angle 1={100}^o$
• B. $\angle 5={100}^o$
• C. $\angle 1={50}^o$
• D. $\angle 5={50}^o$

Answer 1

Answer: (A), (B)

The correct options are
A $\angle 1={100}^o$
B $\angle 5={100}^o$

$\angle 1=\angle 5$ ...... (corresponding angles)
$\Rightarrow \angle 1=(120-x^o)=\angle 5=5x^o$
$\Rightarrow 6x={120}^o$
$\Rightarrow x={20}^o$
$\angle 1=({120}^o-{20}^o)={100}^o$ and $\angle 5=5\times {20}^o={100}^o$