Question

find the remote interior angle measure
find the measure of ∠gef.
multiple choice
what is the measure of ∠gef?
this question is worth 1 point(s)
61 degrees
98 degrees
37 degrees

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(FGE\), \(\angle GFD\) is an exterior angle, so \(m\angle GFD=m\angle FGE + m\angle GEF\).

Step2: Substitute the known values

We know that \(m\angle GFD = 143^{\circ}\) and \(m\angle FGE=82^{\circ}\). Let \(m\angle GEF=x\). Then, according to the exterior angle theorem, we have the equation \(143^{\circ}=82^{\circ}+x\).

Step3: Solve for \(x\)

To find \(x\), we subtract \(82^{\circ}\) from both sides of the equation: \(x = 143^{\circ}-82^{\circ}\).
\(x=61^{\circ}\)

Answer:

61 degrees (the option corresponding to 61 degrees)