Question

7 the sum of the measures of ∠qrt and ∠trs is 180°. what is the value of x? what is the measure of ∠trs?

Explanation:

Step1: Set up the angle sum equation

$\angle QRT + \angle TRS = 180^\circ$
$(x-10) + (4x+20) = 180$

Step2: Simplify the left side

$x - 10 + 4x + 20 = 180$
$5x + 10 = 180$

Step3: Isolate the variable term

$5x = 180 - 10$
$5x = 170$

Step4: Solve for $x$

$x = \frac{170}{5}$
$x = 34$

Step5: Calculate $\angle TRS$

Substitute $x=34$ into $4x+20$:
$4(34) + 20 = 136 + 20 = 156$

Answer:

The value of $x$ is $34$.
The measure of $\angle TRS$ is $156^\circ$.