Question

1. m∠6 = 7x−24 =

m∠7 = 5x + 14 =

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So \(m\angle6 = m\angle7\).
$$7x - 24=5x + 14$$

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides:
$$7x-5x - 24=5x-5x + 14$$
$$2x-24 = 14$$
Add \(24\) to both sides:
$$2x-24 + 24=14 + 24$$
$$2x=38$$
Divide both sides by \(2\):
$$x = 19$$

Step3: Find \(m\angle6\)

Substitute \(x = 19\) into \(m\angle6=7x - 24\):
$$m\angle6=7\times19-24$$
$$m\angle6 = 133-24$$
$$m\angle6=109$$

Step4: Find \(m\angle7\)

Substitute \(x = 19\) into \(m\angle7=5x + 14\):
$$m\angle7=5\times19+14$$
$$m\angle7 = 95 + 14$$
$$m\angle7=109$$

Answer:

\(m\angle6 = 109\), \(m\angle7 = 109\)