Question

5 find the measure of each angle.
find $m\angle qrt$ and $m\angle trs$.
$m\angle qrt = $
$m\angle trs = $

Explanation:

Step1: Set up angle sum equation

The two angles form a straight line, so their sum is $180^\circ$.
$$(3x + 5) + (10x - 7) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$13x - 2 = 180$$
$$13x = 182$$
$$x = 14$$

Step3: Calculate $m\angle QRT$

Substitute $x=14$ into the angle's expression.
$$m\angle QRT = 3(14) + 5 = 42 + 5 = 47$$

Step4: Calculate $m\angle TRS$

Substitute $x=14$ into the angle's expression.
$$m\angle TRS = 10(14) - 7 = 140 - 7 = 133$$

Answer:

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