Question

find the measure of ∠fbh. 2m + 34 7m - 7

Explanation:

Step1: Assume the angle is a right - angle

If \(\angle FBH\) and \(\angle HBM\) form a right - angle (\(90^{\circ}\)), then \((2m + 34)+(7m-7)=90\).

Step2: Combine like terms

\[

$$\begin{align*} 2m+7m+34 - 7&=90\\ 9m + 27&=90 \end{align*}$$

\]

Step3: Isolate the variable term

Subtract 27 from both sides: \(9m=90 - 27=63\).

Step4: Solve for \(m\)

Divide both sides by 9: \(m=\frac{63}{9}=7\).

Step5: Find the measure of \(\angle FBH\)

Substitute \(m = 7\) into the expression for \(\angle FBH\) which is \(2m+34\). So, \(2\times7 + 34=14 + 34=48\).

Answer:

\(48^{\circ}\)