Question

find the measure of ∠mrt.

Explanation:

Step1: Note angle - sum property

Since $\angle MRY = 90^{\circ}$, and $\angle MRT+\angle TRY=\angle MRY$, we have $(6d + 84)+(8d + 90)=90$.

Step2: Combine like - terms

$6d+8d+84 + 90=90$.
$14d+174 = 90$.

Step3: Solve for $d$

Subtract 174 from both sides: $14d=90 - 174$.
$14d=- 84$.
Divide both sides by 14: $d=\frac{-84}{14}=-6$.

Step4: Find $\angle MRT$

Substitute $d = - 6$ into the expression for $\angle MRT$ which is $6d + 84$.
$\angle MRT=6\times(-6)+84$.
$\angle MRT=-36 + 84$.
$\angle MRT = 48^{\circ}$.

Answer:

$48^{\circ}$