Question

22 multiple choice 2 points
in the two triangles, ( ab = xy ), ( ac = xz ), and ( mangle cab = mangle zxy = 110^{circ} ). choose the best answer that explains the relationship between the two triangles.
23 multiple choice 2 points
the measure of an angle is ( 75^{circ} ). what is the measure of its complementary angle?

Explanation:

Question 22

For triangle congruence, the SAS (Side - Angle - Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Here, \(AB = XY\), \(AC = XZ\), and \(\angle CAB=\angle ZXY = 110^{\circ}\). The angle is between the two pairs of equal sides.

Complementary angles add up to \(90^{\circ}\). Let the complementary angle be \(x\). Then \(x + 75^{\circ}=90^{\circ}\). Solving for \(x\), we get \(x=90^{\circ}- 75^{\circ}\).

Answer:

congruent by SAS

Question 23