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})
(angle 1congangle 2)
(mangle 2 = 45^{circ})
(angle bag) is a right angle
(angle 1 & angle 2) are complementary

Explanation:

Step1: Analyze the right - angle property

Since \( \overrightarrow{GA}\perp\overrightarrow{GB}\), by the definition of perpendicular lines, \(m\angle AGB = 90^{\circ}\).

Step2: Analyze the straight - angle property

Given that \( \angle FGC\) is a straight angle (\(m\angle FGC=180^{\circ}\)), and \( \angle FGC=\angle1 + \angle AGB+\angle2\). Substituting \(m\angle AGB = 90^{\circ}\) into the equation \(180^{\circ}=\angle1 + 90^{\circ}+\angle2\), we get \(\angle1+\angle2 = 90^{\circ}\), so \( \angle1\) and \( \angle2\) are complementary.

Step3: Check the measure of \( \angle2\)

Since \( \angle1+\angle2 = 90^{\circ}\), if \( \angle1=\angle2\) (from the complementary relationship and symmetry in the absence of other angular constraints in the perpendicular - straight - angle setup), then \(2\angle2=90^{\circ}\), so \(m\angle2 = 45^{\circ}\)

Answer:

\(m\angle AGB = 90^{\circ}\), \(m\angle2 = 45^{\circ}\), \(\angle1\cong\angle2\), \(\angle1\) and \(\angle2\) are complementary.