Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(65 + 2y+3y = 180\).

Step2: Combine like terms

Combine the \(y\) - terms: \(65+(2 + 3)y=180\), which simplifies to \(65 + 5y=180\).

Step3: Isolate the term with \(y\)

Subtract \(65\) from both sides: \(5y=180 - 65\). Then \(5y = 115\).

Step4: Solve for \(y\)

Divide both sides by \(5\): \(y=\frac{115}{5}\).

Answer:

\(y = 23\)