Question

the diagram shows a triangle. angles are 12y, 16y+12°, 12y+8°. what is the value of y? y = \boxed{}°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, we add the three angles: \(12y + (12y + 8^\circ) + (16y + 12^\circ) = 180^\circ\).

Step2: Combine like terms

Combine the \(y\)-terms and constant terms: \(12y + 12y + 16y + 8 + 12 = 180\), which simplifies to \(40y + 20 = 180\).

Step3: Solve for \(y\)

Subtract 20 from both sides: \(40y = 180 - 20 = 160\). Then divide by 40: \(y = \frac{160}{40} = 4\).

Answer:

\(y = 4\)