Measuring and Drawing Lines and Angles

Compare the angle with a right angle and with a straight line.

Find where the right-hand end of the line is. Each small mark on the ruler is 1 millimetre, which is 0.1 cm.

Read the position of each end of the line, then subtract. Remember that 1 cm is 10 mm.

One arm of the angle lies along the line through 0. Use the scale that starts at 0 on that arm.

Is angle y more or less than half a turn? Look at the angle on the other side of the arms.

One arm of the angle lies along the line through 0 on the left. Use the scale that starts at 0 on that side.

1. The left arm of the angle passes through 0 on the outer scale, so use the outer scale.
2. The other arm crosses the outer scale one small mark after 120. The small marks go up in 10s.
3. x=130°. (Reading 50° from the inner scale is a common mistake: the angle is obtuse.)

There are 10 millimetres in 1 centimetre.

1. 1 cm =10 mm.
2. 5.8\times10=58, so 5.8 cm =58 mm.

Decide whether each angle is acute, obtuse or reflex.

1. Q is less than a right angle, so it is acute.
2. P is between a right angle and a straight line, so it is obtuse.
3. R is more than a straight line (180°), so it is reflex.
4. Acute angles are the smallest and reflex angles the largest: Q, P, R.

Find 4 cm on the ruler, then count on 3 small marks. Each small mark is 1 mm.

1. 4.3 cm is 4 cm and 3 mm.
2. Find the 4 on the ruler and count 3 small marks to the right.
3. That is point C. (B is at 4.7 cm, D is at 3.4 cm and A is at 2.8 cm.)

Asha's line goes through 0 on the inner scale, so count round on the inner scale.

1. Asha's line is on the right, through 0 on the inner scale. Use the inner scale.
2. Count round from 0: 10, 20, 30, 40. Line B goes through 40 on the inner scale.
3. Line A goes through 40 on the outer scale, but that angle is 140° from Asha's line.
4. The answer is line B.

Find the arm that lies along the baseline. Which scale has 0 on that arm?

1. The lower arm lies along the baseline, through 0 on the inner scale. So use the inner scale.
2. The other arm crosses the inner scale two small marks after 90. The small marks go up in 10s.
3. x=110°. This makes sense: the angle is obtuse. (70°, from the outer scale, would be acute.)

Read the position of each point on the ruler. Each small mark is 1 mm, which is 0.1 cm.

Part (a)

1. P is at 0 cm.
2. Q is 6 small marks past 1 cm, at 1.6 cm.
3. PQ =1.6 cm.

Part (b)

1. R is 4 small marks past 4 cm, at 4.4 cm.
2. QR =4.4-1.6=2.8 cm.

Look at where the left-hand end of the line is.

1. The line does not start at 0. Its left end is at 1 cm and its right end is at 6 cm.
2. Length =6-1=5 cm.
3. Tom read the right-hand end only. The line is 5 cm long because it starts at 1 cm, not 0.

First measure the smaller angle between the two arms. The angles all the way round a point add up to 360°.

1. The right arm passes through 0 on the inner scale, so read the inner scale.
2. The other arm crosses the inner scale two small marks after 120, so the smaller angle is 140°.
3. Angles round a point add up to 360°.
4. r=360-140=220°.

Both angles are measured from the arm through 0 on the inner scale. Angle y does not start at 0.

Part (a)

1. The right arm is on 0 of the inner scale.
2. The middle arm crosses the inner scale at 50, so x=50°.

Part (b)

1. The left arm crosses the inner scale at 130.
2. Angle y runs from 50 to 130, so y=130-50=80°.

Read the length of AB from the ruler first. Then change 12 mm into centimetres.

1. A is at 0 and B is 6 small marks past 4 cm, so AB =4.6 cm.
2. 12 mm =1.2 cm, so BC =4.6+1.2=5.8 cm.
3. Perimeter =4.6+5.8+2.5=12.9 cm.

She needs a line to measure the angle from, before she can use the protractor.

1. First she needs a line to work from, so step Q comes first: draw AB.
2. Next she measures the angle at A with the protractor: step P.
3. Then she draws the line through the 50° mark and measures 5 cm along it to find C: step R.
4. Finally she joins B to C: step S.
5. The order is Q, P, R, S.

First work out what each long mark and each short mark is worth. Count the gaps between the long marks from 0 to 20.

1. There are 10 gaps between long marks from 0 to 20, so each long gap is 20÷10=2 cm.
2. Each long gap is split into 4 small gaps, so each small gap is 2÷4=0.5 cm.
3. The line ends 3 small marks after the 6th long mark.
4. Length =6\times2+3\times0.5=12+1.5=13.5 cm.

Measure both lines on the ruler first. Then use the scale: each centimetre on the plan is 10 m in real life.

1. The path to the shed is 4.8 cm on the plan.
2. The path to the pond is 2.3 cm on the plan.
3. Difference on the plan =4.8-2.3=2.5 cm.
4. Real difference =2.5\times10=25 m.

Read angle BAC from the scale that has 0 on AB. The angles in a triangle add up to 180°.

Part (a)

1. AB passes through 0 on the inner scale, so read the inner scale.
2. AC crosses the inner scale one small mark after 30, so angle BAC =40°.

Part (b)

1. The angles in a triangle add up to 180°.
2. Angle ACB =180-40-45=95°.

Part (c)

1. 95° is more than 90° and less than 180°, so angle ACB is obtuse.
2. It looks close to a right angle, but the working shows it is 95°.