Question

use your knowledge of the angles around parallel lines to find all of the angles in each figure, given just one. 1) 2) 3) 4)

Explanation:

Step1: Identify vertical angles

Vertical angles are equal.

Step2: Identify supplementary angles

Supplementary angles sum to \(180^{\circ}\).

Step3: Identify corresponding angles (for parallel lines)

Corresponding angles are equal when lines are parallel.

For Figure 1:

• The angle vertical to \(62^{\circ}\) is \(62^{\circ}\).
• The supplementary angles to \(62^{\circ}\) are \(180 - 62=118^{\circ}\), and their vertical angles are also \(118^{\circ}\).

For Figure 2:

• The angle vertical to \(137^{\circ}\) is \(137^{\circ}\).
• The supplementary angles to \(137^{\circ}\) are \(180 - 137 = 43^{\circ}\), and their vertical angles are also \(43^{\circ}\).

For Figure 3:

• The angle vertical to \(98^{\circ}\) is \(98^{\circ}\).
• The supplementary angles to \(98^{\circ}\) are \(180 - 98=82^{\circ}\), and their vertical angles are also \(82^{\circ}\).

For Figure 4:

• The angle vertical to \(39^{\circ}\) is \(39^{\circ}\).
• The supplementary angles to \(39^{\circ}\) are \(180 - 39 = 141^{\circ}\), and their vertical angles are also \(141^{\circ}\).

Answer:

1. Angles: \(62^{\circ}, 118^{\circ}, 62^{\circ}, 118^{\circ}\)
2. Angles: \(137^{\circ}, 43^{\circ}, 137^{\circ}, 43^{\circ}\)
3. Angles: \(98^{\circ}, 82^{\circ}, 98^{\circ}, 82^{\circ}\)
4. Angles: \(39^{\circ}, 141^{\circ}, 39^{\circ}, 141^{\circ}\)