Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2y)+(2y - 33^{\circ})+(y-12^{\circ})=180^{\circ}\).

Step2: Combine like terms

Combine the \(y\) - terms and the constant terms: \(2y+2y + y-(33^{\circ}+12^{\circ})=180^{\circ}\), which simplifies to \(5y-45^{\circ}=180^{\circ}\).

Step3: Solve for \(y\)

Add \(45^{\circ}\) to both sides: \(5y=180^{\circ}+45^{\circ}\), so \(5y = 225^{\circ}\). Then divide both sides by \(5\): \(y=\frac{225^{\circ}}{5}\).

Answer:

\(y = 45\)