Question

what is the value of m?

Explanation:

Step1: Analyze the relationship between angles

We know that the sum of angles around a point is \(360^{\circ}\), and there is a right - angle (\(90^{\circ}\)) in the figure. Also, vertical angles are equal.

Step2: Calculate the value of \(m\)

Since the sum of angles around a point: \(m + 90^{\circ}+32^{\circ}+ \text{(vertical angle of }m)+ \text{(vertical angle of }32^{\circ})+ \text{(vertical angle of }90^{\circ})=360^{\circ}\). But using the property of complementary angles (assuming the non - labeled angles are such that we can use a simpler approach).
We know that \(m + 90^{\circ}+32^{\circ}= 180^{\circ}\) (because they form a straight - line pair of angles).

$$m=180^{\circ}-90^{\circ}-32^{\circ}$$

$$m = 58^{\circ}$$

Answer:

\(58\)