Question

the diagram shows a triangle. the triangle has angles 2y, y - 19°, and y - 17°. what is the value of y? y = \boxed{\space}°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, we add the three angles: \(2y + (y - 19^\circ) + (y - 17^\circ) = 180^\circ\).

Step2: Simplify the equation

Combine like terms: \(2y + y + y - 19 - 17 = 180\) → \(4y - 36 = 180\).

Step3: Solve for y

Add 36 to both sides: \(4y = 180 + 36 = 216\). Then divide by 4: \(y = \frac{216}{4} = 54\).

Answer:

\(54\)