Question

label (on the diagram) all angles in the diagram. 9)

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The angle opposite to the \(30^{\circ}\) angle is \(30^{\circ}\), and the angle opposite to the \(62^{\circ}\) angle is \(62^{\circ}\).

Step2: Use the triangle angle - sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). For the lower - right triangle, let the unknown angle be \(x\). Then \(x + 37^{\circ}+(180^{\circ}- 62^{\circ})=180^{\circ}\). First, simplify \(180^{\circ}-62^{\circ}=118^{\circ}\). So the equation becomes \(x + 37^{\circ}+118^{\circ}=180^{\circ}\). Combine like terms: \(x+(37^{\circ}+118^{\circ})=180^{\circ}\), \(x + 155^{\circ}=180^{\circ}\). Subtract \(155^{\circ}\) from both sides: \(x=180^{\circ}-155^{\circ}=25^{\circ}\).

Answer:

The unknown angle is \(25^{\circ}\)