Test: Lines and Angles - Class 7 MCQ

• When two lines intersect, they form four angles at the intersection point.
• The angles that are opposite each other are called vertically opposite angles.
• For example, if one angle measures 30 degrees, the angle directly across from it will also measure 30 degrees.
• This equality occurs due to the way angles are formed by intersecting lines, ensuring that vertically opposite angles are always equal.

• Two angles forming a linear pair are adjacent, sharing a common side.

• The non-common sides lie on a straight line, which measures 180 degrees.
• This means the sum of the two angles is 180 degrees.
• Angles that add up to 180 degrees are called supplementary.

A line that intersects two or more lines at distinct points is called transversal

A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.

If two angles are supplementary then the sum of their measures is 180^°

If two angles are complementary, then the sum of their measures is 90^°.

∠S and 100° form a linear pair i.e, 

∠S + 100° = 180°

∠S = 180deg - 100°

∠S = 80°

Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.

So in the given figure ∠2, ∠3 are alternate interior angles
Alternate angle form Z shape

Let the angle be x
measure of its complement = (90-x)
measure of its supplement= (180-x)
7(90-x) =3(180-x)-10

630 - 7x=540x-3x -10

-7x+3x= 530-630
-4x=-100

x= 100/4
x=25º

Linear pair has a sum of 180 degrees
So x+61 =180 degrees
x = 180 - 61 =119 degrees

When we talk about angles around a point, imagine you are standing in one spot and you look all the way around in a full circle. As you turn around completely, you would have covered 360 degrees. This is because a full rotation or circle measures 360 degrees. Therefore, the sum of all angles formed by lines meeting at a single point (all the way around that point) adds up to 360 degrees.

Here's a simple way to think about it:

• If you take four right angles (each 90 degrees) and place them together around a point, they will form a full circle.
• 90^∘+90^∘+90^∘+90^∘=360^∘

So, no matter how many angles you have around a point, their total will always be 360 degrees.

If  two lines are intersected by a transversal such that any pair of corresponding angles are equal then the lines are parallel

Its a straight angle which is equal to 180 degrees.
So ,6y+y+2y = 180
9y = 180
y= 180/9 = 20 degrees

• (a) This is true.
  By the property of parallel lines and transversals, corresponding angles are always equal.

• (b) This is true.
  Alternate interior angles are equal when a transversal cuts two parallel lines.

• (c) This is true.
  Interior angles on the same side of the transversal are supplementary, meaning their sum is 180°.

• (d) This is false.
  A transversal intersects two parallel lines at exactly two points, not three.