Question

what is the value of u?

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

u = □

Explanation:

Step1: Apply 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, \(45u - 11=(14u + 25)+35\).

Step2: Simplify the equation

First, simplify the right - hand side: \((14u + 25)+35=14u+60\). Then the equation becomes \(45u - 11 = 14u+60\).

Step3: Isolate the variable \(u\)

Subtract \(14u\) from both sides: \(45u-14u - 11=14u - 14u+60\), which gives \(31u-11 = 60\). Then add \(11\) to both sides: \(31u-11 + 11=60 + 11\), so \(31u=71\).

Step4: Solve for \(u\)

Divide both sides by \(31\): \(u=\frac{71}{31}\approx2.3\).

Answer:

\(u = 2.3\)