Question

1. ∠1 and ∠2 are vertical angles. if ( mangle1=(17x + 1)^{circ} ) and ( mangle2=(20x - 14)^{circ} ), find ( mangle2 ).

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(m\angle1 = m\angle2\).
$$17x + 1=20x-14$$

Step2: Solve the equation 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 \(m\angle2\)

Substitute \(x = 5\) into the expression for \(m\angle2=(20x - 14)^{\circ}\)
$$m\angle2=(20\times5-14)^{\circ}=(100 - 14)^{\circ}=86^{\circ}$$

Answer:

\(86^{\circ}\)