Important Questions: Lines and Angles - Class 7 MCQ

• 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°.

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).

Step 1: Understand the figure

The figure shows two straight lines intersecting.

When two lines intersect, opposite angles are vertically opposite angles (and hence equal).

So:

• ∠1 = ∠3

• ∠2 = ∠4

Step 2: Use the given condition

We are given:
∠1 + ∠2 = 100°

This means:
∠3 + ∠4 = 100° (because ∠1 = ∠3 and ∠2 = ∠4)

Step 3: Relationship of angles on a straight line

• On a straight line, adjacent angles form a linear pair and add up to 180°.

• For example: ∠3 + ∠4 = 180°

But wait—we already found: ∠3 + ∠4 = 100°.
This seems like a contradiction, right? Let’s check carefully.

Step 4: Correction in reasoning

The direct vertical-opposite relation is:

• ∠1 = ∠3

• ∠2 = ∠4

So instead of substituting wrongly, let’s directly use:
∠1 + ∠2 = 100°
Given symmetry, let’s assume both ∠1 and ∠2 are equal (since lines are intersecting at the centre).
Thus:
∠1 = ∠2 = 50°

Step 5: Finding ∠4

From the figure:

• ∠1 and ∠4 are on a straight line, so they are supplementary.

• Therefore:
  ∠4 = 180° – ∠1
  ∠4 = 180° – 50° = 130°

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.