Question

what is the value of y?

write your answer as an integer or as a decimal rounded to the nearest tenth.

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, \(4y+(8y - 48)=8y + 14\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4y+8y-48=8y + 14\), which simplifies to \(12y-48=8y + 14\).

Step3: Move the terms with \(y\) to one side

Subtract \(8y\) from both sides: \(12y-8y-48=8y-8y + 14\), resulting in \(4y-48=14\).

Step4: Isolate \(y\)

Add \(48\) to both sides: \(4y-48 + 48=14+48\), so \(4y=62\). Then divide both sides by \(4\): \(y=\frac{62}{4}=15.5\).

Answer:

\(y = 15.5\)