Question

which equation can be used to find the measure of ehg?
( m widehat { ehg } + 80 + 35 = 180 )
( m widehat { ehg } + 80 + 35 = 360 )
( m widehat { ehg } - 80 - 35 = 360 )
( m widehat { ehg } - 80 - 35 = 180 )

Explanation:

Step1: Recall the total degree of a circle

The total degree measure around a circle is \(360^{\circ}\).

Step2: Analyze the given arcs and the arc \(\overset{\frown}{EHG}\)

Let the measure of arc \(\overset{\frown}{EHG}\) be \(m\overset{\frown}{EHG}\). The other two arcs have measures \(80^{\circ}\) and \(35^{\circ}\).
Since \(m\overset{\frown}{EHG}+80 + 35=360\) (sum of all arcs in a circle is \(360^{\circ}\))

Answer:

\(m\overset{\frown}{EHG}+80 + 35=360\) (the second option)