Lines and Angles

Vidya is enjoying her time on the swing. She notices that the greater the angle with which she starts the swinging, the greater is the speed she achieves on her swing. But where is the angle? Are you able to see any angle?

Draw and label an angle with arms ST and SR.

Make any figure with three acute angles, one right angle and two obtuse angles.

Draw the letter 'Y' such that the three angles formed are 150°, 60° and 150°.

Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease. a. How many right angles do you have now? Justify why the angles are exact right angles. b. Describe how you folded the paper so that any other person who doesn't know the process can simply follow your description to get the right angle.

Find the degree measures of different angles in your classroom using your protractor.

Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C, D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C, D? Write them all down, and mark each of them with a curve as in Fig. 2.9.

Rihan marked a point on a piece of paper. How many lines can he draw that pass through the point? Sheetal marked two points on a piece of paper. How many different lines can she draw that pass through both of the points? Can you help Rihan and Sheetal find their answers?

The angle of a door: Is it possible to express the amount by which a door is opened using an angle? What will be the vertex of the angle and what will be the arms of the angle?

The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? What is the largest acute angle formed between two spokes?

Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure?

Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the angles formed between the fold and the sides of the paper. Make different angles by folding a rectangular sheet of paper and compare the angles. Which is the largest and smallest angle you made?

How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?

Draw a rough figure and write labels appropriately to illustrate each of the following: a. OP and OQ meet at O. b. XY and PQ intersect at point M. c. Line l contains points E and F but not point D. d. Point P lies on AB.

Explain why APC cannot be labelled as P.

Make a few acute angles and a few obtuse angles. Draw them in different orientations.

Use a protractor to draw angles having the following degree measures: a. 110° b. 40° c. 75° d. 112° e. 134°

Draw angles with the following degree measures: a. 140° b. 82° c. 195° d. 70° e. 35°

Angles in a clock: a. The hands of a clock make different angles at different times. At 1 o'clock, the angle between the hands is 30°. Why? b. What will be the angle at 2 o'clock? And at 4 o'clock? 6 o'clock? c. Explore other angles made by the hands of a clock.

Draw the letter 'M' such that the angles on the sides are 40° each and the angle in the middle is 60°.