Question

In the diagram of circle R, m FGH is 50. what is mFEH

Answer 1

Options

• 130°
• 230°
• 260°
• 310°

Answer:

(B)$m\angle FEH=230^\circ$

Step-by-step explanation:

We know that the External Angle = Half the Difference of the Two Arcs

Therefore:

Since FGH is the exterior angle and FEH and FH are the two arcs, then:

$\dfrac12 (\angle FEH-\angle FH)=50^\circ\\\\\angle FEH- \angle FH=100^\circ$

Also:

$\angle FEH+ \angle FH=360^\circ$

Adding the two equations, we have:

$\angle FEH- \angle FH+(\angle FEH+ \angle FH)=360^\circ+100^\circ\\2\angle FEH=460^\circ\\ Divide both sides by 2\\Therefore\\m\angle FEH=230^\circ$