in the diagram of circle r, m∠fgh is 50°. what is mfeh? 130° 230° 260° 310°
in the diagram of circle r, m∠fgh is 50°. what is mfeh? 130° 230° 260° 310°
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. Here, $\angle FGH$ is an inscribed angle and it intercepts arc $\overset{\frown}{FH}$. So, $m\angle FGH=\frac{1}{2}m\overset{\frown}{FH}$. Given $m\angle FGH = 50^{\circ}$, then $m\overset{\frown}{FH}=2\times m\angle FGH$. $m\overset{\frown}{FH}=2\times50^{\circ}=100^{\circ}$
Step2: Find the measure of arc $\overset{\frown}{FEH}$
The sum of the measures of the arcs of a circle is $360^{\circ}$. Let $m\overset{\frown}{FEH}=x$. We know that $m\overset{\frown}{FH}+m\overset{\frown}{FEH}=360^{\circ}$. Since $m\overset{\frown}{FH} = 100^{\circ}$, then $x=360^{\circ}-m\overset{\frown}{FH}$. $x = 360^{\circ}- 100^{\circ}=260^{\circ}$
Answer:
$260^{\circ}$