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, \((c + 20)+4c+5c=180\).

Step2: Combine like terms

Combine the terms with \(c\): \((1 + 4+5)c+20 = 180\), which simplifies to \(10c+20 = 180\).

Step3: Isolate the term with \(c\)

Subtract \(20\) from both sides: \(10c=180 - 20\), so \(10c=160\).

Step4: Solve for \(c\)

Divide both sides by \(10\): \(c=\frac{160}{10}\).

Answer:

\(16\)