Question

a triangle has interior angle measures of 54°, 60°, and 3u + 9°. what is the value of u? write your answer as an integer or as a decimal rounded to the nearest tenth. u =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation \(54 + 60+(3u + 9)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(54+60 + 9+3u=180\), which gives \(123 + 3u=180\).

Step3: Isolate the variable term

Subtract 123 from both sides of the equation: \(3u=180 - 123\), so \(3u = 57\).

Step4: Solve for \(u\)

Divide both sides of the equation by 3: \(u=\frac{57}{3}=19\).

Answer:

19