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 ∠xpz 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 help me solve this view an example get more help -

Explanation:

Step1: Recall linear - pair and congruence concepts

A linear - pair of angles are supplementary (sum to 180°). Equal - complements theorem states that if two angles are complements of the same angle, they are congruent. Right - angles congruent theorem states that all right - angles are congruent.

Step2: Analyze option A

There is no information given in the problem that \(\angle XPZ\) and \(\angle YPZ\) are congruent. So, option A is incorrect.

Step3: Analyze option B

\(\angle XPW\) and \(\angle XPZ\) form a linear pair. A linear pair of angles are supplementary, not congruent. So, option B is incorrect.

Step4: Analyze option C

There is no information suggesting that \(\angle XPZ\) and \(\angle XPW\) are congruent based on the equal - complements theorem. So, option C is incorrect.

Step5: Analyze option D

If \(\angle YPZ\) and \(\angle YPW\) are right - angles (assumed from the context of the right - angles congruent theorem), then by 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