Question

Indicate which pairs of angles are:
Vertically opposite angles.

• A. 1 & 4
• B. 2 & 4
• C. 1 & 3
• D. 5 & 4

Answer 1

The correct option is A 1 & 4

Considering $\angle 1=x$ & $\angle 5=5x$

$x+5x={180}^o$

$\Rightarrow x={30}^o$

$\angle 1=x={30}^o$

$\angle 5=5x={150}^o$

Being vertically opposite angles,

$\angle 5=\angle 3+\angle 2$

${150}^o=\angle 3+\angle 2$

${90}^o+{60}^o={150}^o$

$\angle 3={90}^o$

$\angle 2={60}^o$

$\angle 4+\angle 3+\angle 2={180}^o$

$\angle 4=180-(\angle 3+\angle 2)$

$=180-(90+60)$

$={30}^o$

$\angle 1=\angle y={30}^o$

$\therefore 1$ & $4$ are vertically opposite.