Free download NCERT Solutions for Class 9 Maths Chapter 6 exercise 6.1, 6.2, 6.3 of lines and angles (geometry) in PDF form. Solutions for class IX maths for all chapters are given in downloadable form to assist the students.

## NCERT Solutions for Class 9 Maths Chapter 6

### Definition of different types of angle

**Acute angle**: An angle measure between 0° and 90°.**Right angle**: Angle exactly equal to 90°.**Obtuse angle**: An angle greater than 90° but less than 180°.**Straight angle**: An angle exactly equal to 180°.**Reflex Angle**: An angle greater than 180° but less than 360°.**Complimentary Angles**: A pair of angles whose sum is 90°.**Supplementary angle**: A pair of angles whose sum is 180°.**Adjacent angles**: Two angles are adjacent if (i) They have a common vertex. (ii) a common arm (iii) Their non common arms are on opposite sides of common arm.

### Class 9 Maths – Lines and Angles

#### Questions with Answers for Exams practice

- If an angle is equal to its complement find the angle. [Answer: 45]
- One of the angle of a pair of supplementary angles is 23 more than its supplement find the angles. [Answer: 86 and 94]
- By contributing money 5 friends bought pizza. They want to divide it equally among themselves. But one of them was given double piece, as he was very hungry. Find the angle of the piece of pizza each one received. [Answer: 4 pieces of 60 angle and one piece of 120 angle]
- BO and CO are external bisector of angle B and angle C of a ∆ABC intersecting at O. If angle A = 60° and angle ABC = 70°, find angle BOC.
- In the above question 15, if Internal bisector of angle B and angle C intersect at P. Prove that angle PBO = 90° and angle BOC + angle BPC = 180°.
- An exterior angle of triangle is 103° and two of its interior opposite angles are equal, find the angles. [Answer: 51.5 and 51.5]
- Prove that vertically opposite angles are equal.
- The angle of a triangle are (x – 40°), (x – 20°), (x/2 – 10). Find the value of x and then find the angles of the triangle. [Answer: x = 100, angles of triangles are 60, 80 and 40]
- If the angle of triangle are in the ratio 5:3:7 then show that the triangle is acute angled triangle.
- Two lines are respectively perpendicular to two parallel lines show that they are parallel to each other.
- Prove that the bisector of the angles of a linear pair are at right angle.
- If two complementary angles are such that two times the measure of one is equal to three times the measure of the other. Find the measure of larger angle. [Answer: 54]
- Prove that the sum of all exterior angles of a triangle is 360°.
- If the bisectors of angle Q and angle R of a triangle angle PQR meet at points, then prove that angle QSR = 90 + 1/2 (angle P).
- If a transversal intersects two parallel lines prove that internal bisectors of the angle on the same side of a transversal meet at right angles.
- Prove that quadrilateral formed by the intersection of bisectors of interior angles made by a transversal on two parallel lines is a rectangle.