Question

the diagram shows a triangle. what is the value of c? c = °

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((c + 28^{\circ})+(c + 30^{\circ})+114^{\circ}=180^{\circ}\).

Step2: Combine like terms

Combine the \(c\) terms and the constant terms: \(2c+(28 + 30+114)^{\circ}=180^{\circ}\), which simplifies to \(2c + 172^{\circ}=180^{\circ}\).

Step3: Solve for \(c\)

Subtract \(172^{\circ}\) from both sides: \(2c=180^{\circ}-172^{\circ}\), so \(2c = 8^{\circ}\). Then divide both sides by \(2\): \(c=\frac{8^{\circ}}{2}\).

Answer:

\(4\)