Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(48^{\circ}+4y + 2y=180^{\circ}\).

Step2: Combine like terms

Combine the \(y\) - terms: \(48+(4 + 2)y=180\), which simplifies to \(48 + 6y=180\).

Step3: Isolate the term with \(y\)

Subtract \(48\) from both sides: \(6y=180 - 48\). So, \(6y=132\).

Step4: Solve for \(y\)

Divide both sides by \(6\): \(y=\frac{132}{6}\).

Answer:

\(y = 22\)