Question

what is the value of y?
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Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(y + 35^{\circ}=(y - 37^{\circ})+(y - 41^{\circ})\).

Step2: Expand the right - hand side

Expand \((y - 37^{\circ})+(y - 41^{\circ})\) to get \(y-37 + y - 41=2y-78\). So the equation becomes \(y + 35=2y-78\).

Step3: Solve for \(y\)

Subtract \(y\) from both sides: \(35=y - 78\). Then add \(78\) to both sides: \(y=35 + 78=111\).

Answer:

\(111\)