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Parallel lines and angles
Dynamic tasks on corresponding, alternate interior and same-side interior angles, including comprehension of geometric relationships.
Questions: 10Estimated time: 15 minutes
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Question 1out of 10
A transversal crosses two lines. Corresponding angles are 78° and 78°. What can be concluded?
If corresponding angles formed by a transversal are equal, the lines are parallel. If they are unequal, the lines are not parallel. Compare the given measures.
Question 2out of 10
One same-side interior angle is 131°. Find the other same-side interior angle.
Interior angles on the same side of a transversal, or on the same trapezoid leg between parallel bases, total 180°. Subtract the known angle from 180° to find the other.
Question 3out of 10
Which statement about corresponding angles formed by parallel lines is always true?
When a transversal crosses parallel lines, corresponding angles are equal. They occupy matching positions at the two intersections, so the required angle has the same measure as the known one.
Question 4out of 10
Same-side interior angles are 62° and 118°. What is their sum?
Add the two given angle measures. Same-side interior angles of parallel lines total 180°; the calculation lets you check that relationship.
Question 5out of 10
Same-side interior angles are (x + 6)° and x°. Their total measure is 180°. Find x.
Add the two given angles: (x + b) + x = total angle. Thus 2x + b = total angle, so x = (total angle − b) ÷ 2.
Question 6out of 10
Which angles lie between two parallel lines and on the same side of the transversal?
“Interior” means the angles lie between the two lines. “Same-side” means both are on the same side of the transversal. These are therefore same-side interior angles.
Question 7out of 10
One alternate interior angle is 59°. Find the equal alternate interior angle. The lines are parallel.
Alternate interior angles of parallel lines are equal. They lie between the lines on opposite sides of the transversal. The required angle equals the given angle.
Question 8out of 10
One alternate interior angle is 86°. Find the equal alternate interior angle. The lines are parallel.
Alternate interior angles of parallel lines are equal. They lie between the lines on opposite sides of the transversal. The required angle equals the given angle.
Question 9out of 10
A transversal crosses two parallel lines. One corresponding angle is 140°. Find the other corresponding angle.
When a transversal crosses parallel lines, corresponding angles are equal. They occupy matching positions at the two intersections, so the required angle has the same measure as the known one.
Question 10out of 10
Same-side interior angles are (x + 6)° and x°. Their total measure is 180°. Find x.
Add the two given angles: (x + b) + x = total angle. Thus 2x + b = total angle, so x = (total angle − b) ÷ 2.
Time left: 00:00:00
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Sample questions
- A transversal crosses two parallel lines. One corresponding angle is ___°. Find the other corresponding angle.
- One alternate interior angle is ___°. Find the equal alternate interior angle. The lines are parallel.
- One same-side interior angle is ___°. Find the other same-side interior angle.
- Same-side interior angles are (x + ___)° and x°. Their total measure is ___°. Find x.
- Which statement about corresponding angles formed by parallel lines is always true?
Parallel lines and angles
When a transversal crosses parallel lines, corresponding and alternate interior angles are equal, while same-side interior angles total 180°. These relationships determine angles without measurement.
Working method
Mark the known angle, identify its relationship with the unknown and then use equality or supplementation to 180°. Vertically opposite angles at an intersection are also equal.
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