Question

In the circle below, suppose arc FEH= 234 and

Answer 1

The value of arc FEH is 234 degrees i.e the major arc FH subtends an angle of 234 degrees at the center.

The value of angle subtended by the major arc FH at the circle will be the half of angle subtended by it on the center,

$\begin{gathered} \angle\text{FGH}=\frac{234^{\circ}}{2} \\ =117^{\circ} \end{gathered}$

Simirally the angle subtended by the minor arc FG on the center is 109 hence it will subtend half angle at the circle,

$\begin{gathered} \angle EHG=\frac{109^{\circ}}{2} \\ =54.5^{\circ} \end{gathered}$

The value of angle FEH

$\begin{gathered} \angle FEH+\angle FGH=180 \\ \angle FEH+117=180 \\ \angle FEH=63^{\circ} \end{gathered}$

Thus, the required value of angle FEH is 63 degrees and the value of angle EHG is 54.5 degrees.