Question

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

Explanation:

Step1: Use the triangle angle sum theorem

The sum of angles in a triangle is \(180^{\circ}\). So, \(10x + 54^{\circ}+78^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

\(10x+(54 + 78)^{\circ}=180^{\circ}\), which gives \(10x + 132^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(132^{\circ}\) from both sides: \(10x=180^{\circ}-132^{\circ}\), so \(10x = 48^{\circ}\). Then divide both sides by \(10\): \(x=\frac{48^{\circ}}{10}=4.8^{\circ}\).

Answer:

\(x = 4.8\)