Question

in the diagram of circle r, m∠fgh is 50°. what is m⌢eh? 130° 230° 260° 310°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, the inscribed angle $\angle FGH = 50^{\circ}$, and the arc it intercepts is $\overset{\frown}{FH}$. So, $m\overset{\frown}{FH}=2\times m\angle FGH$.
$m\overset{\frown}{FH}=2\times50^{\circ}=100^{\circ}$

Step2: Find the measure of $\overset{\frown}{EH}$

The sum of the measures of the arcs of a circle is $360^{\circ}$. We know that $m\overset{\frown}{EH}+m\overset{\frown}{FH}=360^{\circ}$. Let $m\overset{\frown}{EH}=x$. Then $x + 100^{\circ}=360^{\circ}$.
$x=360^{\circ}- 100^{\circ}=260^{\circ}$

Answer:

$260^{\circ}$