Fundamental Concepts of Geometry — Assertion-Reason Type Questions

Assertion (A): There are some figures in geometry which have both curvilinear and linear boundary.

Reason (R): Curvilinear means having curved line, linear means straight line.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Figures such as a semicircle have both a curved boundary and a straight boundary, so some geometrical figures do have both curvilinear and linear boundaries. So, Assertion (A) is true.

Curvilinear means having a curved line and linear means a straight line. So, Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A): The angles around a point are: a right angle, x - 10° and 2x + 40°. Then the value of x is 40°.

Reason (R): The sum of all angles around a point is 360°.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

The sum of all the angles around a point is 360°.

⇒ 90° + (x − 10°) + (2x + 40°) = 360°

⇒ 3x + 120° = 360°

⇒ 3x = 360° − 120°

⇒ 3x = 240°

⇒ x = $\dfrac{240\degree}{3}$

⇒ x = 80°

Since x = 80° and not 40°, Assertion (A) is false.

The sum of all angles around a point is 360°. So, Reason (R) is true.

Hence, option 2 is the correct option.