Question

what is the value of m?

Explanation:

Step1: Use the fact that the sum of angles around a point is \(360^{\circ}\)

We know that \(57^{\circ}+90^{\circ}+33^{\circ}+m = 180^{\circ}\) (since the angles are on a straight - line, sum of angles on a straight - line is \(180^{\circ}\))

Step2: Simplify the left - hand side

First, add the known angles: \(57 + 90+33=(57 + 33)+90=90 + 90 = 180\)
So, \(180+m = 180\)

Step3: Solve for \(m\)

Subtract \(180\) from both sides: \(m=180-(57 + 90+33)=180 - 180=30\)

Answer:

\(30\)