Question

∠1 and ∠2 are vertical angles. if m∠1 = (6x + 11)° and m∠2 = (10x - 9)°, find the m∠1.
x=
m∠1= degrees

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(6x + 11=10x - 9\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(11 = 4x-9\).
Add \(9\) to both sides: \(20 = 4x\).
Divide both sides by \(4\): \(x = 5\).

Step3: Find \(m\angle1\)

Substitute \(x = 5\) into \(m\angle1=(6x + 11)^{\circ}\).
\(m\angle1=(6\times5 + 11)^{\circ}=(30 + 11)^{\circ}=41^{\circ}\).

Answer:

\(x = 5\), \(m\angle1 = 41\) degrees.