Question

what is the value of u?

u =

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, \(u + 48=(u + 17)+(6u-47)\).

Step2: Simplify the right - hand side of the equation

First, expand the right - hand side: \((u + 17)+(6u-47)=u+17 + 6u-47=7u-30\).
So the equation becomes \(u + 48=7u-30\).

Step3: Solve for \(u\)

Subtract \(u\) from both sides: \(48=7u - u-30\), which simplifies to \(48 = 6u-30\).
Add \(30\) to both sides: \(48 + 30=6u\), so \(78 = 6u\).
Divide both sides by \(6\): \(u=\frac{78}{6}=13\).

Answer:

\(13\)