Question

1. 5y - 7 47° (6x + 5)°

Explanation:

Step1: Find \(x\) using vertical angles

Vertical angles are equal. So \(6x + 5=47\).
Subtract \(5\) from both sides: \(6x=47 - 5\), \(6x = 42\).
Divide both sides by \(6\): \(x=\frac{42}{6}=7\).

Step2: Find \(y\) using linear - pair angles

Angles in a linear pair sum to \(180^{\circ}\). So \(5y-7 + 47=180\).
Simplify the left - hand side: \(5y+40 = 180\).
Subtract \(40\) from both sides: \(5y=180 - 40\), \(5y = 140\).
Divide both sides by \(5\): \(y=\frac{140}{5}=28\).

Answer:

\(x = 7\) and \(y = 28\)