Question

1. given a parallelogram pqrs, ∠pqr is 24.

a. draw parallelogram pqrs and label it.
b. what is the angle measure of ∠rsp? explain how you know.
c. what is the angle measure of ∠qrs? explain how you know.

1. in a quadrilateral mnop, mp is congruent to on, and mp is parallel to on. andre has written a proof to show that mnop is a parallelogram. fill in the blanks to complete the proof. since mp is parallel to __, alternate interior angles and nom are congruent. mo is congruent to since segments are congruent to themselves. along with the given information that mp is congruent to on, triangle pmo is congruent to by the triangle congruence. since the triangles are congruent, all pairs of corresponding angles are congruent, so angle pom is congruent to . since those alternate interior angles are congruent, mn must be parallel to __. since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, mnop is a parallelogram.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - angles are equal.

Step2: Find $\angle RSP$

Since $\angle PQR$ and $\angle RSP$ are opposite angles in parallelogram $PQRS$ and $\angle PQR = 24^{\circ}$, then $\angle RSP=\angle PQR = 24^{\circ}$.

Step3: Recall adjacent - angles property

In a parallelogram, adjacent angles are supplementary (their sum is $180^{\circ}$).

Step4: Find $\angle QRS$

$\angle PQR$ and $\angle QRS$ are adjacent angles. Let $\angle QRS=x$. We know that $\angle PQR+\angle QRS = 180^{\circ}$. Given $\angle PQR = 24^{\circ}$, then $x=180 - 24=156^{\circ}$. So $\angle QRS = 156^{\circ}$.

Answer:

b. The measure of $\angle RSP$ is $24^{\circ}$ because opposite angles in a parallelogram are equal.
c. The measure of $\angle QRS$ is $156^{\circ}$ because adjacent angles in a parallelogram are supplementary ($\angle PQR+\angle QRS = 180^{\circ}$ and $\angle PQR = 24^{\circ}$).