Question

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

Explanation:

Step1: Use the triangle - angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(7a + 11a+72^{\circ}=180^{\circ}\).

Step2: Combine like terms

\((7 + 11)a+72^{\circ}=180^{\circ}\), which simplifies to \(18a+72^{\circ}=180^{\circ}\).

Step3: Isolate the term with \(a\)

Subtract \(72^{\circ}\) from both sides: \(18a=180^{\circ}-72^{\circ}\). So, \(18a = 108^{\circ}\).

Step4: Solve for \(a\)

Divide both sides by \(18\): \(a=\frac{108^{\circ}}{18}\).

Answer:

\(6\)