Question

the diagram shows a convex polygon.
what is the value of u?
u = □°

Explanation:

Step1: Find the sum of angles on a straight line

A straight line forms a \(180^\circ\) angle. For each \(150^\circ\) angle, the adjacent interior angle is \(180 - 150 = 30^\circ\). So we have two angles of \(30^\circ\) each.

Step2: Use the sum of angles in a triangle

The sum of angles in a triangle is \(180^\circ\). Let the angles be \(30^\circ\), \(30^\circ\), and \(3u\). So \(30 + 30 + 3u = 180\).
Simplify: \(60 + 3u = 180\).
Subtract 60: \(3u = 180 - 60 = 120\).
Divide by 3: \(u = \frac{120}{3} = 40\).

Answer:

\(40\)