Question

1. if \\( \angle goh = 24 ^ { \circ } \\) and \\( \angle foh = 50 ^ { \circ } \\), what is the measure of \\( \angle fog \\)?

a. 31
b. 28
c. 23
d. 26

1. \\( \angle 1 \\) and \\( \angle 2 \\) are supplementary angles. \\( \angle 1 \\) and \\( \angle 3 \\) are vertical angles. if \\( \angle 2 = 72 ^ { \circ } \\) find the measure of \\( \angle 3 \\).

a. 18
b. 72
c. 108
d. 28

Explanation:

Step1: Analyze the relationship between angles

From the figure, we know that \(\angle FOH=\angle FOG + \angle GOH\).

Step2: Solve for \(\angle FOG\)

We can rewrite the formula as \(\angle FOG=\angle FOH-\angle GOH\).
Substitute \(\angle GOH = 24^{\circ}\) and \(\angle FOH = 50^{\circ}\) into the formula: \(\angle FOG=50^{\circ}- 24^{\circ}\).

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Step1: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary angles, we know that \(\angle1+\angle2 = 180^{\circ}\). Given \(\angle2 = 72^{\circ}\), then \(\angle1=180^{\circ}-\angle2\).

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Step2: Use the property of vertical angles

Since \(\angle1\) and \(\angle3\) are vertical angles, and vertical angles are equal. So \(\angle3=\angle1\).

Answer:

D. 26