Question

line cd with ∠gfc and ∠gfd are shown. which could be measures for ∠gfd and ∠cfg? o m∠gfc = 78° and m∠gfd = 92° o m∠gfc = 60° and m∠gfd = 130° o m∠gfc = 12° and m∠gfd = 78° o m∠gfc = 62° and m∠gfd = 118°

Explanation:

Step1: Recall angle - addition property

Since $\angle GFD+\angle GFC = 180^{\circ}$ (linear - pair of angles, they are supplementary), we need to check which pairs of angles add up to 180 degrees.

Step2: Check each option

• Option 1: $62^{\circ}+118^{\circ}=180^{\circ}$
• Option 2: $12^{\circ}+78^{\circ}=90^{\circ}

eq180^{\circ}$

• Option 3: $60^{\circ}+130^{\circ}=190^{\circ}

eq180^{\circ}$

• Option 4: $78^{\circ}+92^{\circ}=170^{\circ}

eq180^{\circ}$

Answer:

$m\angle GFC = 62^{\circ}$ and $m\angle GFD = 118^{\circ}$