Question

In the figure(not drawn to scale), AHB, CHD and EHF are straight lines. Find x.

• A. ${25}^o$
• B. ${16}^o$
• C. ${27}^o$
• D. ${28}^o$

Answer 1

The correct option is B ${16}^o$

Given that $AHB,CHD$ and $EHF$ are straight lines.

$\angle CHE=\angle FHD={50}^{\circ }$ ....Vertically opposite angles

$\angle AHB={180}^{\circ }$ AHB is a straight line.

$\angle AHB={72}^{\circ }+\angle CHE+{42}^{\circ }+x={180}^{\circ }$

Substitute value of angle $CHE$, we get

${72}^{\circ }+{50}^{\circ }+{42}^{\circ }+x={180}^{\circ }$

$\Rightarrow {164}^{\circ }+x={180}^{\circ }$

$\Rightarrow x={16}^{\circ }$