Question

find the measure of each angle.
(3x + 5)° (10x - 7)°
q r s
m∠qrt=
m∠trs=

Explanation:

Step1: Set up equation

Since $\angle QRT$ and $\angle TRS$ are a linear - pair, their sum is $180^{\circ}$. So, $(3x + 5)+(10x-7)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $3x+10x + 5-7=180$, which simplifies to $13x-2 = 180$.

Step3: Solve for $x$

Add 2 to both sides of the equation: $13x=180 + 2=182$. Then divide both sides by 13: $x=\frac{182}{13}=14$.

Step4: Find $m\angle QRT$

Substitute $x = 14$ into the expression for $\angle QRT$: $m\angle QRT=3x + 5=3\times14+5=42 + 5=47^{\circ}$.

Step5: Find $m\angle TRS$

Substitute $x = 14$ into the expression for $\angle TRS$: $m\angle TRS=10x-7=10\times14-7=140-7 = 133^{\circ}$.

Answer:

$m\angle QRT = 47^{\circ}$
$m\angle TRS = 133^{\circ}$