Question

1. ∠1 and ∠2 are vertical angles. if ( m angle 1=(17 x+1)^{circ} ) and ( m angle 2=(20 x-14)^{circ} ), find ( m angle 2 )

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we have \(17x + 1=20x-14\).

Step2: Solve for \(x\)

Subtract \(17x\) from both sides: \(1 = 3x-14\).
Add \(14\) to both sides: \(15=3x\).
Divide both sides by \(3\): \(x = 5\).

Step3: Find \(m\angle1\)

Substitute \(x = 5\) into \(m\angle1=17x + 1\).
\(m\angle1=17\times5+1=85 + 1=86^{\circ}\).

Step4: Find \(m\angle2\)

Since \(m\angle2=m\angle1\) (vertical angles), \(m\angle2 = 86^{\circ}\).

Answer:

\(m\angle1 = 86^{\circ}\), \(m\angle2=86^{\circ}\)