GSEB Class 6 Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.3

Question 1. Name the angles in the given figure.

Answer: The angles in the given shape are:
(i) \( \angle A \) or \( \angle DAB \)
(ii) \( \angle B \) or \( \angle ABC \)
(iii) \( \angle C \) or \( \angle DCB \)
(iv) \( \angle D \) or \( \angle ADC \)
In simple words: In the given shape, the angles are found at each corner. We can call them by their single letter name or by using three letters with the corner letter in the middle.

Exam Tip: When naming angles in a polygon, always ensure the vertex (corner) letter is in the middle of the three-letter notation to correctly identify the angle.

 

Question 2. In the given diagram, name the point (s)
(a) in the interior of \( \angle DOE \)
(b) in the exterior of \( \angle EOF \)
(c) on \( \angle EOF \)

Answer:
(a) The point inside \( \angle DOE \) is A.
(b) The points outside \( \angle EOF \) are A, C, and D.
(c) The points located on \( \angle EOF \) are E, B, O, and F.
In simple words: We look at the angle formed by two rays meeting at a point. 'Interior' means inside the angle, 'exterior' means outside it, and 'on the angle' means on its boundary lines or vertex.

Exam Tip: Remember that points "on" an angle include the vertex and any points along its two rays. Points in the interior are strictly between the rays, and points in the exterior are outside the region formed by the rays.

 

Question 3. Draw rough diagrams of two angles such that they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.

Answer:
(a) In the figure below, \( \angle PQS \) and \( \angle RQS \) have one point Q in common.

(b) In the figure below, \( \angle DOB \) and \( \angle ODC \) have two points O and D in common.

(c) It is not possible for two angles to share exactly three distinct points. If they share more than two points that are not on the same line, they will generally share an infinite number of points or be the exact same angle. If the three points are collinear, they would form a line segment, which also contains infinitely many points, not just three.
(d) It is not possible for two angles to share exactly four distinct points. Similar to having three points in common, if two angles share four or more specific points, it typically means they significantly overlap or are identical, leading to an infinite count of shared points rather than a precise number like four.
(e) In the figure below, \( \angle RQS \) and \( \angle PQS \) have one ray \( \overline{QS} \) in common.

In simple words: When two angles share common parts, they can share only their meeting point (vertex), a line segment (like two points), or an entire ray. Sharing exactly three or four isolated points without sharing a complete line or region is geometrically not possible under standard definitions.

Exam Tip: Understand the definitions of points, rays, and angles clearly. Visualizing how two angles can overlap or intersect helps in determining the number of common elements.