Question

created by parallel lines cut by a transversal. for each set of angles name the angle pair and find the missing measurement. type of angle pair. these angles are. so... x = _. 5) type of angle pair. these angles are. so... x = _. 6) type of angle pair. these angles are. so... x = _. 7) type of angle pair. these angles are. so... x = _. 8) type of angle pair. these angles are. so... x = _.

Explanation:

Step1: Identify angle - pair types

When parallel lines are cut by a transversal, there are several types of angle - pairs: corresponding angles, alternate interior angles, alternate exterior angles, and same - side interior angles. Corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and same - side interior angles are supplementary (sum to 180°).

Step2: Solve for \(x\) in each case

Case 1:

If the angles are corresponding angles (or alternate interior/exterior angles), they are equal. If they are same - side interior angles, they add up to 180°.
For the first pair with 68° and \(x\):

• Type of angle pair: Corresponding angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x = 68\).

Case 2:

For the pair with 77° and \(x\):

• Type of angle pair: Alternate interior angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x=77\).

Case 3:

For the pair with 134° and \(x\):

• Type of angle pair: Alternate exterior angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x = 134\).

Case 4:

For the pair with 106° and \(x\):

• Type of angle pair: Corresponding angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x = 106\).

Case 5:

For the pair with 120° and \(x\):

• Type of angle pair: Same - side interior angles (assuming the typical parallel - line and transversal setup).
• These angles are supplementary. So \(x=180 - 120=60\).

Case 6:

For the pair with 74° and \(x\):

• Type of angle pair: Corresponding angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x = 74\).

Case 7:

For the pair with 101° and \(x\):

• Type of angle pair: Alternate exterior angles (assuming the typical parallel - line and transversal setup).
• These angles are equal. So \(x = 101\).

Case 8:

For the pair with 142° and \(x\):

• Type of angle pair: Same - side interior angles (assuming the typical parallel - line and transversal setup).
• These angles are supplementary. So \(x=180 - 142 = 38\).

Answer:

1. Type of angle pair: Corresponding angles. These angles are equal. \(x = 68\).
2. Type of angle pair: Alternate interior angles. These angles are equal. \(x = 77\).
3. Type of angle pair: Alternate exterior angles. These angles are equal. \(x = 134\).
4. Type of angle pair: Corresponding angles. These angles are equal. \(x = 106\).
5. Type of angle pair: Same - side interior angles. These angles are supplementary. \(x = 60\).
6. Type of angle pair: Corresponding angles. These angles are equal. \(x = 74\).
7. Type of angle pair: Alternate exterior angles. These angles are equal. \(x = 101\).
8. Type of angle pair: Same - side interior angles. These angles are supplementary. \(x = 38\).