Lines and Angles — Hard

Q1. Consider these statements about angles: I. Doubling both arms of an angle doubles its measure. II. Two angles can be equal even with different arm lengths. III. An angle's size depends on the rotation between its arms. Which are correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q2. In a figure, angle AOB is formed by rays OA and OB and angle XOB is formed by rays OX and OB. The ray OX lies between OA and OB. Which of the following is true?

• A. Angle AOB is smaller than angle XOB
• B. Angle AOB and angle XOB are always equal
• C. Angle AOB is larger than angle XOB because XOB is a part of AOB
• D. Angle XOB is larger than angle AOB

Q3. On a straight line AOB, a ray OC is drawn such that angle AOC equals angle COB. The measure of angle AOC is

• A. 45°
• B. 60°
• C. 90°
• D. 120°

Q4. Two lines that meet each other at a right angle are called

• A. Parallel lines
• B. Perpendicular lines
• C. Intersecting curves
• D. Equal lines

Q5. In the chapter, a large equilateral triangle contains 1 inner triangle (Fig. 1), then 3 inner triangles (Fig. 2). How many acute angles does Fig. 2 contain in total?

• A. Three
• B. Six
• C. Nine
• D. Twelve

Q6. Priya draws the letter ‘M’ so that the two side angles are each 40° and the middle angle is 60°. How are these three angles classified?

• A. All three are right angles
• B. All three are acute angles
• C. Two are obtuse and one is acute
• D. Two are acute and one is reflex

Q7. In a figure, an unmarked acute angle measures 100°. The reflex angle on the other side at the same vertex measures

• A. 80°
• B. 100°
• C. 180°
• D. 260°

Q8. A straight angle is bisected, the resulting angle is bisected again, and this halving is repeated one more time. The measure of the final angle is

• A. 90°
• B. 60°
• C. 45°
• D. 22.5°

Q9. If the bisector of a right angle is drawn, the measure of each of the two equal angles formed is

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Q10. Assertion (A): The measure of one degree is 1/360 of a full turn. Reason (R): A full turn has been divided by mathematicians into 360 equal angular parts. Which of the following is correct?

• A. Both A and R are true, and R is the correct explanation of A
• B. Both A and R are true, but R is NOT the correct explanation of A
• C. A is true, R is false
• D. A is false, R is true

Q11. A circle is divided into 8 equal parts at its centre. The angle measure of each part is

• A. 30°
• B. 40°
• C. 45°
• D. 60°

Q12. On the outer scale of a protractor, one arm of an angle passes through 20° and the other arm passes through 55°. The measure of the angle is

• A. 20°
• B. 35°
• C. 55°
• D. 75°

Q13. At a vertex Q on a protractor base PT, three rays QR, QS and QT are drawn so that angle PQR = 45°, angle PQS = 100° and angle PQT = 150°. The measure of angle RQT equals

• A. 45°
• B. 55°
• C. 105°
• D. 150°

Q14. A student wants to use her self-made paper protractor (a half-circle from 0° to 180°) to measure an angle of 260°. Which conclusion is correct?

• A. The paper protractor will give the reading directly as 260°
• B. The paper protractor cannot show 260° directly because it has only 0° to 180° markings
• C. The paper protractor will give the reading as 80°, which is the correct measure
• D. The angle 260° does not exist, so no protractor is needed

Q15. The Ashoka Chakra has 24 equally spaced spokes. The angle between two adjacent spokes, and the largest acute angle between any two spokes, are respectively

• A. 15° and 75°
• B. 15° and 90°
• C. 24° and 60°
• D. 30° and 90°