Question

In the given figure, AB // CD, EH // BC, $\angle BAC={60}^{\circ }$ and $\angle DGH={40}^{\circ }$. Find the measures of $\angle AFG$.

• A. ${96}^o$
• B. ${86}^o$
• C. ${100}^o$
• D. none of the above

Answer 1

The correct option is C ${100}^o$

Given that $\angle BAC={60}^o$ and $\angle DGH={40}^o$.

$⟹$ $\angle EAF={60}^o$.

Also, given, $AE\parallel DG$.

Now, $\angle AEF=\angle DGH={40}^{\circ }$ (Corresponding angles).
Then, $\angle AFG=\angle AEF+\angle EAF$ (Exterior angle property)

$⟹$ $\angle AFG={40}^{\circ }+{60}^{\circ }$

$⟹$ $\angle AFG={100}^{\circ }$.

Therefore, option $C$ is correct.