Important Questions: Lines and Angles for Class 7 Maths - Free MCQ Test

• A linear pair consists of two adjacent angles whose non-common sides form a straight line.
• A straight line measures 180°.
• Therefore, the sum of the measures of the angles in a linear pair is 180°.
• This is because the angles add up to form a straight line, which is always 180°.
• Thus, the correct answer is B: 180°.

We have two parallel lines aaa and bbb, cut by a transversal ccc. Angles are formed at AAA (with line aaa) and at BBB (with line bbb).

Step 1: Rules to recall

• Corresponding angles are equal
• Alternate interior angles are equal
• Vertically opposite angles are equal
• Linear pair of angles are supplementary, not equal

Step 2: Check each option
a) ∠1 and ∠2
These are adjacent angles at A and form a linear pair. They are supplementary, not equal. Hence, they need not be equal.

b) ∠1 and ∠3
These are vertically opposite angles at A. They are always equal.

c) ∠1 and ∠5
These are corresponding angles (∠1 at A, ∠5 at B). For parallel lines, they are equal.

d) ∠2 and ∠8
These are alternate interior angles. For parallel lines, they are equal.

Final Answer: a) ∠1 and ∠2

120° + 60° = 180°.

• Vertically opposite angles are formed when two lines intersect.
• These angles are always equal to each other.
• Options A, B, and C are true because vertically opposite angles can be both acute, obtuse, or right angles, as long as they are equal.
• Option D is false because vertically opposite angles are always equal.
• Therefore, statement D is incorrect.

Look at the figure carefully. Two straight lines AB and CD intersect at O, forming four angles. One of them is given as 62°. We are asked to find the value of x – y.

Step 1: Relationship of x and 62°
x and the given 62° are on the same straight line. Angles on a straight line add up to 180°.
So, x + 62° = 180°
x = 180° – 62° = 118°.

Step 2: Relationship of y and 62°
y and the given 62° are opposite to each other at the intersection. Opposite (vertically opposite) angles are always equal.
So, y = 62°.

Step 3: Find x – y
x – y = 118° – 62° = 56°.

Final Answer: 56° (option a).

Given:
∠1 + ∠2 = 100°
Step 1: Use complete angle formula
All four angles around a point add up to 360°:
∠1+∠2+∠3+∠4 = 360^∘
Step 2: Use vertically opposite angle property
∠1 = ∠2
∠3 = ∠4
Let ∠4 = x 
So, Also ∠3 = x
As, ∠1+∠2+∠3+∠4 = 360^∘
100º + x + x = 360º
2x = 360º - 100º
2x = 260º
x = 260º ÷ 2
x = 130º
Therefore, ∠3 = ∠4 = 130º
Correct Option: D

To find the supplement, subtract the given angle from 180°:

• Calculation: 180° - 120° = 60°

The supplement of the angle is 60°.

• Linear Pair Definition: A linear pair consists of two adjacent angles whose non-common sides form a straight line.
• Supplementary Angles: Angles that add up to 180 degrees are called supplementary angles.
• Relation to Linear Pair: Since the non-common sides of a linear pair form a straight line, the angles together measure 180 degrees, making them supplementary.

Thus, the angles in a linear pair are supplementary.

Let the angle be x degrees. Its complement is (90 - x) degrees. According to the problem, the angle is double its complement:

x = 2(90 - x).

Expanding and solving for x:

• x = 180 - 2x
• 3x = 180
• x = 60

Thus, the measure of the angle is 60°.

• When the sum of the measures of two angles is 90°, these angles are called complementary angles.
• Complementary angles can be adjacent or non-adjacent, but their sum is always 90°.
• Supplementary angles sum up to 180°, not 90°.
• Adjacent angles share a common side and vertex but aren't defined by their sum.
• Vertically opposite angles are formed by intersecting lines and are equal, not defined by a specific sum.

To find the complement of a 30° angle, follow these steps:

• Complementary angles sum to 90°.
• Subtract the given angle from 90°.

So, the calculation is:

90° - 30° = 60°

Therefore, the complement of a 30° angle is 60°.

correct answer: D ∠2 + ∠6 = 180°

Step-by-Step Verification

1. Option (a): ∠1 + ∠2 = 180°

   • ∠1 and ∠2 are a linear pair at point G (on line l).

   • Linear pair sum = 180°. ✅ Correct

2. Option (b): ∠2 + ∠5 = 180°

   • ∠2 and ∠5 are interior angles on the same side of the transversal.

   • Property: For parallel lines, co-interior angles sum = 180°. ✅ Correct

3. Option (c): ∠3 + ∠8 = 180°

   • ∠3 (bottom left at G) and ∠8 (top left at H).

   • They are also co-interior angles.

   • So, ∠3 + ∠8 = 180°. ✅ Correct

4. Option (d): ∠2 + ∠6 = 180°

   • ∠2 (bottom right at G) and ∠6 (bottom right at H).

   • These are corresponding angles, and for parallel lines they are equal, not supplementary.

   • So ∠2 = ∠6, not ∠2 + ∠6 = 180°. ❌ False

60°+ 30° = 90°.

The solution is based on the concept of complementary angles.

• Complementary angles are two angles whose measures add up to 90°.
• This means the sum of the measures of these angles is always 90°.

Supplementary angles are those which sum up to be 180°

In options a, b and c, the sum of the two angles is 180°

In option d

120° + 90° = 210° ≠ 180°.

Thus angles in option d are not supplementary.