Question

what is the value of y?
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y =

Explanation:

Step1: Apply 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, \(43y - 32=22y + 13y\).

Step2: Simplify the right - hand side

Simplify \(22y + 13y\) to get \(35y\). The equation becomes \(43y-32 = 35y\).

Step3: Isolate the variable \(y\)

Subtract \(35y\) from both sides: \(43y-35y-32=35y - 35y\), which simplifies to \(8y-32 = 0\). Then add \(32\) to both sides: \(8y-32 + 32=0 + 32\), so \(8y=32\).

Step4: Solve for \(y\)

Divide both sides by \(8\): \(y=\frac{32}{8}\).

Answer:

\(y = 4\)