Question

name two pairs of congruent angles in the figure. justify the answer. select all that apply. a. ∠xpz and ∠ypz as given in the figure b. ∠xpw and ∠zpx according to the linear - pair theorem c. ∠xpz and ∠xpw according to the equal complements theorem d. ∠ypz and ∠ypw according to the right angles congruent theorem

Explanation:

Step1: Recall congruent - angles theorems

Congruent angles have equal measures. The Linear - Pair Theorem states that if two angles form a linear pair, they are supplementary. The Equal Complements Theorem states that if two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. The Right - Angles Congruent Theorem states that all right angles are congruent.

Step2: Analyze option A

There is no information given that \(\angle XPZ\) and \(\angle YPZ\) are congruent just from the figure without further angle - measure information.

Step3: Analyze option B

\(\angle XPW\) and \(\angle XPZ\) form a linear pair according to the Linear - Pair Theorem. A linear pair of angles are supplementary (\(\angle XPW+\angle XPZ = 180^{\circ}\)), not congruent.

Step4: Analyze option C

There is no information indicating that \(\angle XPZ\) and \(\angle XPW\) are complements of the same angle, so the Equal Complements Theorem does not apply here.

Step5: Analyze option D

If \(\angle YPZ\) and \(\angle YPW\) are right angles (assuming from the context or if it can be deduced), then according to the Right - Angles Congruent Theorem, all right angles are congruent, so \(\angle YPZ\cong\angle YPW\).

Answer:

D. \(\angle YPZ\) and \(\angle YPW\) according to the Right Angles Congruent Theorem