Question

the diagram shows a triangle. what is the value of u? u =

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2u - 49)+(2u - 49)+(2u - 34)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2u+2u + 2u-49-49 - 34=180\), which is \(6u-(49 + 49+34)=180\). Then \(6u - 132 = 180\).

Step3: Solve for \(u\)

Add \(132\) to both sides of the equation: \(6u=180 + 132\), so \(6u=312\). Divide both sides by \(6\): \(u=\frac{312}{6}\).

Answer:

\(u = 52\)