Parallel and Intersecting Lines - Class 7 Mathematics Olympiad Free MCQ

When two parallel lines are intersected by a transversal, the corresponding angles are equal. 

If angle a measures 120°, then angle b can be calculated as follows:

• Angles a and b form a linear pair, which means they are supplementary.
• Supplementary angles add up to 180°.
• To find angle b, subtract angle a from 180°:
• b = 180° - 120° = 60°.

Therefore, the measure of angle b is 60°.

If the alternate interior angles formed by a transversal intersecting two lines are equal, it can be concluded that those two lines are parallel. 

Vertically opposite angles are formed when two lines intersect. These angles are opposite each other at the intersection point and are always equal, which is a key property in geometry.

Transversal is the term used for a line that intersects two or more other lines. This type of line creates various angles and can help in understanding relationships between the intersected lines.

The interior angles on the same side of a transversal that intersects two parallel lines are supplementary, meaning they add up to 180°. 

When two lines are perpendicular, they meet each other at a right angle.
A right angle measures 90°

At the point where the two perpendicular lines cross:

• They form four angles
• All four angles are equal 
• Each angle is a right angle, so each measures 90°

Therefore, the correct answer is: Option C 90°

A linear pair of angles consists of two adjacent angles whose non-common arms form a straight line, meaning their measures add up to 180°. In other words, the two angles are next to each other (adjacent) and together form a straight angle. This is the correct definition of a linear pair, so option d is correct.

The term intersecting lines refers to two lines that cross each other at one point, known as the point of intersection.

• The original angle is 90°.
• After increasing by 10°, it becomes 100°.
• Angles in a linear pair sum to 180°.
• Adjacent angle = 180 - 100 = 80°.

Therefore, the measure of the angle adjacent to the increased angle is 80°.

Let the smaller angle be x.
Then the larger angle = 3x

Since they form a linear pair:
x + 3x = 180°
4x = 180°
x = 180° ÷ 4
x = 45°

So, the angles are 45° and 135°

Two adjacent angles whose sum is 180° form a linear pair.

Parallel lines are defined as lines that never meet or intersect, regardless of how far they are extended. 

Exterior angles are the angles that lie outside the region between the two lines and are formed at the intersections where the transversal crosses each line.