Question

1. if ∠a and ∠b are vertical angles and m∠a = 30, what is m∠b?
2. if ∠a and ∠b are a linear pair and m∠a = 2x + 8 and m∠b = 3x + 2, what is the value of x? x=
3. if ∠a and ∠b are vertical angles and m∠a = 7x - 5 and m∠b = 4x + 10, what is the value of x? x=

Explanation:

Step1: Recall the property of vertical angles

Vertical angles are equal. So if ∠A and ∠B are vertical angles, then m∠A = m∠B. Given m∠A=7x - 5 and m∠B = 4x + 10, we set up the equation 7x−5=4x + 10.

Step2: Solve the equation for x

Subtract 4x from both sides: 7x−4x−5=4x−4x + 10, which simplifies to 3x−5=10. Then add 5 to both sides: 3x−5 + 5=10 + 5, getting 3x=15. Divide both sides by 3: $\frac{3x}{3}=\frac{15}{3}$, so x = 5.

Answer:

5