Question

1. ∠u and ∠w are vertical angles. if m∠u=(6x + 11)° and m∠w=(10x - 9)°, find m∠u.

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set \(m\angle U=m\angle W\). So, \(6x + 11=10x-9\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(11 = 4x-9\). Then add 9 to both sides: \(20=4x\). Divide both sides by 4, we get \(x = 5\).

Step3: Find \(m\angle U\)

Substitute \(x = 5\) into the expression for \(m\angle U\), \(m\angle U=6x + 11=6\times5+11=30 + 11=41^{\circ}\).

Answer:

\(41^{\circ}\)