Question

find the measure of ∠tbk.

Explanation:

Step1: Set up equation

Since the sum of angles $\angle RBK$ and $\angle KBT$ is $90^{\circ}$ (right - angle), we have $(7d + 12)+(7d + 22)=90$.

Step2: Combine like - terms

Combining the $d$ terms and the constant terms on the left - hand side gives $14d+34 = 90$.

Step3: Isolate the variable term

Subtract 34 from both sides: $14d=90 - 34$, so $14d=56$.

Step4: Solve for $d$

Divide both sides by 14: $d=\frac{56}{14}=4$.

Step5: Find the measure of $\angle TBK$

Substitute $d = 4$ into the expression for $\angle TBK$ which is $7d + 22$. Then $\angle TBK=7\times4+22$.
Calculate $7\times4+22=28 + 22=50$.

Answer:

$50^{\circ}$