Question

example finding angle measures
given that $m\angle qps = 157^{\circ}$, find $m\angle qpr$ and $m\angle rps$.
solution
step 1 write and solve an equation to find the value of $x$.
$m\angle qps = m\angle qpr + m\angle rps$ angle addition postulate
$157^{\circ}=(\underline{\qquad})^{\circ}+(\underline{\qquad})^{\circ}$ substitute angle measures.
$157 = 6x - 5$ combine like terms.
$\underline{\qquad}=6x$ add 5 to each side.
$\underline{\qquad}=x$ divide each side by 6.

Explanation:

Step1: Substitute angle - measures

$157=(4x + 13)+(2x-18)$

Step2: Combine like - terms

$157=(4x+2x)+(13 - 18)$
$157 = 6x-5$

Step3: Add 5 to each side

$157 + 5=6x-5 + 5$
$162 = 6x$

Step4: Divide each side by 6

$\frac{162}{6}=\frac{6x}{6}$
$27=x$

Step5: Find $m\angle QPR$

$m\angle QPR=(4x + 13)^{\circ}$
Substitute $x = 27$: $m\angle QPR=4\times27+13=108 + 13=121^{\circ}$

Step6: Find $m\angle RPS$

$m\angle RPS=(2x-18)^{\circ}$
Substitute $x = 27$: $m\angle RPS=2\times27-18=54 - 18=36^{\circ}$

Answer:

$m\angle QPR = 121^{\circ}$, $m\angle RPS = 36^{\circ}$