the diagram shows a triangle.\nwhat is the value of $y$?\n$y = \\square^{\\circ}$

Explanation:

Step1: State the triangle angle sum theorem

The sum of the interior angles of any triangle is always $180^{\circ}$.

Step2: Set up the equation for the triangle

$$54^{\circ} + 96^{\circ} + 3y = 180^{\circ}$$

Step3: Simplify the left side of the equation

$$150^{\circ} + 3y = 180^{\circ}$$

Step4: Isolate the term with y

$$3y = 180^{\circ} - 150^{\circ}$$ $$3y = 30^{\circ}$$

Step5: Solve for y

$$y = \frac{30^{\circ}}{3}$$ $$y = 10$$

Answer:

y = 10