Question

question 3(multiple choice worth 1 points)
(07.01 mc)
find the measure of (overparen{df}).
(5x + 10^{circ})
(70^{circ})
(11x + 2^{circ})

Explanation:

Step1: Find the value of \(x\)

Vertical angles are equal. So \(5x + 10=70\)
\(5x=70 - 10\)
\(5x=60\)
\(x = 12\)

Step2: Calculate the measure of \(\overset{\frown}{DF}\)

Substitute \(x = 12\) into \(11x+2\)
\(11x+2=11\times12 + 2\)
\(=132+2\)
\(=134\)
Since \(\angle CGF\) and \(\angle EGD\) are vertical angles, \(\angle CGF=\angle EGD = 70^{\circ}\)
The measure of \(\overset{\frown}{DF}\) is \(134^{\circ}+6^{\circ}=140^{\circ}\) (because \(11x + 2+5x+10+(180 - 2\times70)=360\), but another way: \(\overset{\frown}{DF}=360-(5x + 10)-(70)-(11x+2)\), after \(x = 12\), \(5x+10=70\), \(11x + 2=134\), \(360-70 - 70-134=140\))

Answer:

\(140^{\circ}\)