In Fig. 5.12, lines l and m intersect each other at a point. Which of the following is false?
a. ∠a = ∠b
b. ∠d = ∠c
c. ∠a + ∠d = 180°
d. ∠a = ∠d

Solution:

Given, the lines l and m intersect each other at a point

We have to determine the option which is false.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

From the figure,

The vertically opposite angles are

∠a = ∠b

∠c = ∠d

We know that the linear pair of angles is always equal to 180 degrees.

∠a + ∠d = 180°

∠c + ∠b = 180°

The option a, b and c are true.

∠a ≠ ∠d

Therefore, option d is false.

✦ Try This: What value of y would make AOB a line in Fig., if ∠AOC = 4y and ∠BOC =(6y+30)?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Problem 11

In Fig. 5.12, lines l and m intersect each other at a point. Which of the following is false? a. ∠a = ∠b, b. ∠d = ∠c, c. ∠a + ∠d = 180°, d. ∠a = ∠d

Summary:

In Fig. 5.12, lines l and m intersect each other at a point. The option ∠a = ∠d is false

☛ Related Questions:

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• In Fig. 5.13, POR is a line. The value of a is: a. 40°, b. 45°, c. 55°, d. 60°
• In Fig. 5.14, POQ is a line. If x = 30°, then ∠ QOR is: a. 90°, b. 30°, c. 150°, d. 60°