Question

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

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(8c + 4c+36^{\circ}=180^{\circ}\).

Step2: Combine like terms

First, combine the terms with \(c\): \((8 + 4)c+36^{\circ}=180^{\circ}\), which simplifies to \(12c+36^{\circ}=180^{\circ}\).

Step3: Isolate the term with \(c\)

Subtract \(36^{\circ}\) from both sides: \(12c=180^{\circ}- 36^{\circ}\). So, \(12c = 144^{\circ}\).

Step4: Solve for \(c\)

Divide both sides by \(12\): \(c=\frac{144^{\circ}}{12}\).

Answer:

\(c = 12\)