Question

1. (7x + 3)° (4x + 1)° 65°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(4x + 1=65\).

Step2: Solve the equation for \(x\)

Subtract 1 from both sides: \(4x=65 - 1\), so \(4x = 64\). Then divide both sides by 4: \(x=\frac{64}{4}=16\).

Step3: Check with the other pair of vertical angles

We can also use the other pair of vertical angles. Set \(7x+3\) equal to the angle opposite to it. Substitute \(x = 16\) into \(7x+3\), we get \(7\times16+3=112 + 3=115\). And the angle opposite to it should also be \(115\) (by vertical - angle equality).

Answer:

\(x = 16\)