Question

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

Explanation:

Step1: Use the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(30^{\circ}+(3z + 6)^{\circ}+15z^{\circ}=180^{\circ}\).

Step2: Combine like terms

Combine the \(z\) - terms and the constant terms: \(30+6+(3z + 15z)=180\). Which simplifies to \(36 + 18z=180\).

Step3: Solve for \(z\)

Subtract 36 from both sides: \(18z=180 - 36\). So, \(18z=144\). Then divide both sides by 18: \(z=\frac{144}{18}\).

Answer:

\(z = 8\)