Question

14
30°
x
correct

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the two base angles are equal. Let the two equal angles be \(a\). The sum of angles in a triangle is \(180^{\circ}\). So \(a + a+30^{\circ}=180^{\circ}\).

Step2: Solve the equation

\(2a=180^{\circ}- 30^{\circ}=150^{\circ}\), then \(a = 75^{\circ}\). But wait, no, wait the triangle has two equal - side - marked, so the two non - \(x\) angles are equal. Let the non - \(x\) angles be \(y\). We know \(y = 30^{\circ}\) (wait no, no, the side - marking shows that the two sides adjacent to the \(30^{\circ}\) angle and the other non - \(x\) angle are equal. So the two non - \(x\) angles are equal. Let each non - \(x\) angle be \(y\). Then \(y=30^{\circ}\). Using the angle - sum formula for a triangle \(x + 30^{\circ}+30^{\circ}=180^{\circ}\).

Step3: Calculate \(x\)

\(x=180^{\circ}-(30^{\circ}+30^{\circ})=120^{\circ}\)

Answer:

\(120^{\circ}\)