Question

16.

1. ( x = )

( y = )
17.

1. ( x = )

( y = )
18.

1. ( x = )

( y = )
19.

1. ( x = )

( y = )

Explanation:

16.

Step1: Find \(x\)

When two parallel lines are cut by a transversal, the corresponding angles are equal. Here, \(x\) and the right - angled adjacent angle to \(y\) are corresponding angles. Since the lines are parallel, \(x = 90^{\circ}\) (corresponding angles).

Step2: Find \(y\)

We know that \(y\) is adjacent to a right angle. By the definition of a right angle (an angle equal to \(90^{\circ}\)), \(y = 90^{\circ}\)

Step1: Find \(x\)

When two parallel lines are cut by a transversal, alternate interior angles are equal. Here, \(x\) and \(95^{\circ}\) are alternate interior angles. So \(x = 95^{\circ}\)

Step2: Find \(y\)

\(y\) and \(95^{\circ}\) are supplementary angles (they form a linear pair). Using the formula \(y+95^{\circ}=180^{\circ}\), we get \(y = 180^{\circ}-95^{\circ}=85^{\circ}\)

Step1: Find \(x\)

When two parallel lines are cut by a transversal, alternate interior angles are equal. So \(x = 75^{\circ}\)

Step2: Find \(y\)

\(y\) and \(75^{\circ}\) are supplementary angles (they form a linear pair). Using the formula \(y + 75^{\circ}=180^{\circ}\), we get \(y=180^{\circ}-75^{\circ}=105^{\circ}\)

Answer:

\(x = 90^{\circ}\), \(y=90^{\circ}\)

17.