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 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, \(10u - 9=(5u - 11)+(u + 44)\).

Step2: Simplify the right - hand side

Simplify \((5u - 11)+(u + 44)\):

$$
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$$

So the equation becomes \(10u - 9 = 6u+33\).

Step3: Solve for \(u\)

Subtract \(6u\) from both sides: \(10u-6u - 9=6u - 6u+33\), which gives \(4u-9 = 33\).
Add \(9\) to both sides: \(4u-9 + 9=33 + 9\), so \(4u=42\).
Divide both sides by \(4\): \(u=\frac{42}{4}=10.5\).

Answer:

\(10.5\)