Question

if (overrightarrow{ga}perpoverrightarrow{gb}) at (g) and (angle fgc) is a straight angle. based on this information, which of the following must be true? choose all that apply.(mangle agb = 90^{circ})(mangle 2 = 45^{circ})(angle 1&angle 2) are complementary(angle bag) is a right angle(angle 1congangle 2)

Explanation:

Step1: Analyze \(m\angle AGB = 90^{\circ}\)

Since \(\overrightarrow{GA}\perp\overrightarrow{GB}\) at \(G\), by the definition of perpendicular lines, the angle between them (\(\angle AGB\)) is \(90^{\circ}\). So \(m\angle AGB = 90^{\circ}\) is correct.

Step2: Analyze \(m\angle2 = 45^{\circ}\)

There is no information given in the problem (such as angle - bisector or other relationships) to conclude that \(m\angle2 = 45^{\circ}\). So this is incorrect.

Step3: Analyze \(\angle1\) and \(\angle2\) being complementary

Since \(\angle FGC\) is a straight angle (\(180^{\circ}\)) and \(\angle AGB = 90^{\circ}\), then \(\angle1+\angle2=180^{\circ}-\angle AGB = 90^{\circ}\). By the definition of complementary angles (two angles whose sum is \(90^{\circ}\)), \(\angle1\) and \(\angle2\) are complementary.

Step4: Analyze \(\angle BAG\) being a right - angle

There is no information (such as perpendicular lines or angle measures) to suggest that \(\angle BAG = 90^{\circ}\). So this is incorrect.

Step5: Analyze \(\angle1\cong\angle2\)

There is no information (such as angle - bisector) to conclude that \(\angle1\) and \(\angle2\) have the same measure. So \(\angle1\cong\angle2\) is incorrect.

Answer:

\(m\angle AGB = 90^{\circ}\), \(\angle1\) and \(\angle2\) are complementary.