Question

what is the value of u? u + 30° u - 39° u - 49° u = ° submit

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior angle is \(u + 30^{\circ}\), and the two non - adjacent interior angles are \(u-39^{\circ}\) and \(u - 49^{\circ}\). So, \(u+30=(u - 39)+(u - 49)\).

Step2: Expand the right - hand side

Expand \((u - 39)+(u - 49)\) to get \(u+30=u-39+u - 49\). Combine like terms on the right - hand side: \(u+30 = 2u-88\).

Step3: Solve for \(u\)

Subtract \(u\) from both sides: \(30=2u - u-88\). Then \(30=u - 88\). Add 88 to both sides: \(u=30 + 88\).

Answer:

\(u = 118\)