Question

the diagram shows a triangle. what is the value of x?

Explanation:

Step1: Use triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(36^{\circ}+2x + 2x=180^{\circ}\).

Step2: Simplify the equation

Combine like terms: \(36 + 4x=180\).
Subtract 36 from both sides: \(4x=180 - 36\), so \(4x = 144\).

Step3: Solve for \(x\)

Divide both sides by 4: \(x=\frac{144}{4}\).

Answer:

\(x = 36\)