Question

1. in the diagram, two parallel lines are cut by a transversal. which of the numbered angles measures 152°?
2. youre not sure whether a pair of angles formed by two parallel lines and a transversal are same - side exterior angles or alternate exterior angles. both angles measure 53°. which of the two types must they be? explain.
3. which two angles have the same measure?
4. lines m and n are parallel. find the following angle pairs in the diagram. if you cant find any, write none.

alternate exterior
corresponding angles
same - side exterior
alternate interior
same - side interior

1. two angles are same - side interior angles. the measures of the angles are represented by the expressions 7x + 18 and 10x + 9. what are the two angle measures?

Explanation:

Step1: Recall angle - pair properties

Same - side exterior angles are supplementary (add up to 180°), while alternate exterior angles are congruent (equal in measure).

Step2: Analyze the given angle measures

Given that both angles measure 53°. Since they are equal in measure, they must be alternate exterior angles.

Step3: For question 10

If two parallel lines are cut by a transversal, corresponding angles are equal. In the given figure for question 10, if we assume the lines are parallel and the transversal is as shown, angle 1 and angle 3 are corresponding angles and have the same measure.

Step4: For question 11

• Alternate exterior: ∠1 and ∠5
• Corresponding angles: ∠1 and ∠4, ∠2 and ∠5
• Same - side exterior: none
• Alternate interior: ∠2 and ∠4
• Same - side interior: ∠2 and ∠5

Step5: For question 12

Same - side interior angles are supplementary. So, (7x + 18)+(10x + 9)=180.
Combine like terms: 17x+27 = 180.
Subtract 27 from both sides: 17x=180 - 27=153.
Divide both sides by 17: x = 9.
The first angle: 7x + 18=7×9 + 18=63 + 18 = 81°.
The second angle: 10x + 9=10×9+9 = 90 + 9=99°.

Answer:

For the angles that measure 53°: They are alternate exterior angles.
For question 10: Angle 1 and angle 3 have the same measure.
For question 11:

• Alternate exterior: ∠1 and ∠5
• Corresponding angles: ∠1 and ∠4, ∠2 and ∠5
• Same - side exterior: none
• Alternate interior: ∠2 and ∠4
• Same - side interior: ∠2 and ∠5

For question 12: The angle measures are 81° and 99°.