Question

name andrea a date 10/3/25 period 2 given $overleftrightarrow{rs}paralleloverleftrightarrow{qp}$, what is the value of $x$? find the $mangle srq$. prove that the answer is correct using substitution. the theorem/postulate i used is _. $x = $ _

Explanation:

Step1: Use corresponding - angles property

Since $\overrightarrow{RS}\parallel\overrightarrow{QP}$, the corresponding angles are equal. So, $12x = 108$.

Step2: Solve for $x$

Divide both sides of the equation $12x = 108$ by 12. We get $x=\frac{108}{12}=9$.

Step3: Find $m\angle SRQ$

$\angle SRQ$ and the $108^{\circ}$ - angle are supplementary (linear - pair of angles). So, $m\angle SRQ=180 - 108=72^{\circ}$.

Step4: Proof by substitution

Substitute $x = 9$ into the expression for the angle related to $\overrightarrow{RS}$. The angle measure is $12x=12\times9 = 108^{\circ}$, which is equal to the corresponding angle as expected. The theorem used is the corresponding - angles postulate.

Answer:

$x = 9$, $m\angle SRQ=72^{\circ}$, The theorem/postulate I used is the corresponding - angles postulate.