Question

what is the value of y?

Explanation:

Step1: Apply the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(y + 50^{\circ}=(y + 18^{\circ})+(y + 20^{\circ})\)

Step2: Simplify the equation

Expand the right - hand side: \(y + 50^{\circ}=y + 18^{\circ}+y + 20^{\circ}\)
\(y + 50^{\circ}=2y+38^{\circ}\)

Step3: Solve for \(y\)

Subtract \(y\) from both sides: \(50^{\circ}=2y - y+38^{\circ}\)
\(y = 50^{\circ}-38^{\circ}\)

Answer:

\(y = 12^{\circ}\)