Lines and Angles Class 6 MCQs – Ganita Prakash Chapter 2

A point marks an exact location. It has no length, breadth or height. The small dot used to show it on paper is only a representation, and a capital letter such as P identifies the point.

The straight path from A to B, including A and B, is line segment AB. Its two end points fix its length. A curved route is longer, while a line or ray continues beyond the required path.

Extending AB without end in both directions gives a line. A line has no end points, so its complete picture cannot fit on paper. The drawn portion only represents part of the line.

Two distinct points determine one line. Any straight line passing through both points must follow this same path. Through only one point, however, lines can be drawn in many different directions.

Ray OA and ray OB both start at O and extend in the same direction. Therefore, they represent the same ray. Reversing the letters changes the starting point, so ray AO is not the same ray.

A line segment is a part of a line with two endpoints.

The degree measure of a straight angle 180°

The common starting point is S, so S is the vertex. The vertex must be the middle letter in a three-letter angle name. Thus, the angle can be named ∠TSR or ∠RST.

In ∠DBE, the middle letter B identifies the vertex. Rays BD and BE start at B and form the arms of the angle. D and E are points on those arms.

The possible pairs are AB, AC, AD, BC, BD and CD.
Number of different lines = 6
No three points lie on one line, so none of these pairs gives a line already represented by another pair.

The common vertices and both pairs of arms coincide. The amount of turn from one arm to the other is therefore the same for both angles. This is why superimposition shows that the angles are equal.

An angle measures the turn between its arms, not their lengths. Extending the arms along the same directions does not change that turn.
New angle = original angle = 40°

A beam of light from a lighthouse is an example of a ray.

Reflex angle is larger.

For both arms to fit at the same time, they must lie along the two sides of the slit. This happens when their angle equals the slit angle. Making the arms shorter does not correct a mismatch in angle.

A full turn measures 360°.
Half turn = 360° ÷ 2 = 180°
After a half turn, the two arms lie along a straight line in opposite directions. This forms a straight angle.

A right angle measures 90°, and a full turn measures 360°.
Required fraction = 90/360 = 1/4
Four equal right-angle turns complete one full turn.

The two perpendicular creases divide the full turn around their intersection into four equal angles.
Each angle = 360° ÷ 4 = 90°
So there are four right angles around the point.

An acute angle is greater than 0° and less than 90°.
0° < 75° < 90° So 75° is acute. The other measures represent a right angle, an obtuse angle and a straight angle.

A protractor is used to measure angles in degrees.

The common endpoint of two rays is called Vertex.

An obtuse angle is greater than 90° but less than 180°.
90° < 134° < 180° Therefore, 134° is obtuse. It is larger than a quarter turn but smaller than a half turn.

A reflex angle is greater than 180° and less than 360°.
180° < 195° < 360° Thus, 195° is reflex. A measure of exactly 180° is straight, not reflex.

The protractor measures turns about its centre, so the centre must coincide with the angle vertex. With one arm at 0°, the reading reached by the other arm gives the angle directly on that scale.

Both readings use the same starting direction, so the difference gives the angle between the arms.
Angle = 55° − 20° = 35°
Adding the readings would count turns from the scale’s starting line instead.

A straight angle measures 180°.
Each equal part = 180° ÷ 8 = 22.5°
Checking the result, 8 × 22.5° = 180°, so the eight parts exactly fill the straight angle.

The degree measure of a full rotation is 360°.

A reflex angle is greater than 180° but less than 360°.

Bisecting an angle means dividing it into two equal angles.
Each part = 90° ÷ 2 = 45°
The two parts together give 45° + 45° = 90°, the original right angle.

A clock divides a full turn into 12 equal gaps.
One gap = 360° ÷ 12 = 30°
At 2 o’clock, the smaller angle covers two gaps.
Angle = 2 × 30° = 60°

The minute hand points to 12 and the hour hand points to 4. The shorter route between them covers four equal gaps.
Each gap = 360° ÷ 12 = 30°
Smaller angle = 4 × 30° = 120°

The score measures how far the guess is from the actual angle.
Difference = 49° − 39° = 10°
So the score is 10 points. A smaller difference would give a lower score and a more accurate guess.

The middle letter I is the vertex of ∠TIN. Ray IN is aligned with 0°, and the protractor centre is placed at I. A mark at 30° then locates the direction of ray IT.

Two right angles make a straight angle.

A line can be extended Indefinitely in both directions.

The straight angle ∠BER measures 180°. Ray ET divides it into ∠BET and ∠TER.
∠BET + 80° = 180°
∠BET = 180° − 80° = 100°

The two smaller angles together form the right angle ∠SER.
∠SET + ∠TER = 90°
∠SET = 90° − 80° = 10°
The answer is acute, as expected for a small part of a right angle.

The 24 equal gaps between neighbouring spokes fill one full turn.
Angle of one gap = 360° ÷ 24 = 15°
Thus, every pair of neighbouring spokes makes an angle of 15° at the centre.

One gap between neighbouring spokes = 360° ÷ 24 = 15°.
Acute angles between spokes are 15°, 30°, 45°, 60° and 75°.
The next multiple is 90°, which is a right angle. Therefore, the largest acute angle is 75°.

For 20°, the multiples are 40°, 60°, 80° and 100°.
The first three are less than 90°, so they are acute.
The fifth multiple, 100°, lies between 90° and 180°, so it is obtuse.