Question

unit #2 - warmup problem #3: in the diagram, segments $overline{st}$ and $overline{pq}$ intersect at point r such that $mangle srp = 2x$ and $mangle prt = 7x$. find the value of x algebraically and then find the measures of all angles in the diagram. show all work to receive full credit. answers: x = __ m∠srp = m∠prt = m∠qrt = m∠srq = __

Explanation:

Step1: Use linear - pair property

Since $\angle SRP$ and $\angle PRT$ form a linear - pair, $m\angle SRP + m\angle PRT=180^{\circ}$. So, $2x + 7x=180$.

Step2: Solve for $x$

Combine like terms: $9x = 180$. Then, divide both sides by 9: $x=\frac{180}{9}=20$.

Step3: Find measure of $\angle SRP$

Substitute $x = 20$ into $m\angle SRP = 2x$. So, $m\angle SRP=2\times20 = 40^{\circ}$.

Step4: Find measure of $\angle PRT$

Substitute $x = 20$ into $m\angle PRT = 7x$. So, $m\angle PRT=7\times20 = 140^{\circ}$.

Step5: Use vertical - angle property

$\angle QRT$ and $\angle SRP$ are vertical angles, so $m\angle QRT=m\angle SRP = 40^{\circ}$.
$\angle SRQ$ and $\angle PRT$ are vertical angles, so $m\angle SRQ=m\angle PRT = 140^{\circ}$.

Answer:

$x = 20$
$m\angle SRP = 40^{\circ}$
$m\angle PRT = 140^{\circ}$
$m\angle QRT = 40^{\circ}$
$m\angle SRQ = 140^{\circ}$