Websink Prep UKKS2 Maths reasoning (SATs)Year 6 chaptersMaths reasoning (SATs) textbooksYear 6Browse allPast papersFind a tutorBecome a tutor
SATs practice · Year 6Chapter 5 · Geometry: angles and shapes
Year 6 Maths reasoning (SATs) · Geometry: angles and shapes · Lesson 5.1

Year 6 Maths reasoning (SATs): Angles at a point, on a straight line and vertically opposite

Part of the Year 6 Maths reasoning (SATs) geometry: angles and shapes chapter. Chapter overview · whole chapter on one page

5.1

Angles at a point, on a straight line and vertically opposite

Year 6
Know that angles at a point add to 360 degrees, angles on a straight line add to 180 degrees, and vertically opposite angles are equal (Year 6)
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. Sam is building a bookshelf from wood. The pieces meet at points, and he has to work out the angle that is left over at a corner, so he can cut the last piece correctly.

Rule

Angles at a point add up to 360 degrees. Angles on a straight line add up to 180 degrees.

Vertically opposite angles are equal: when two straight lines cross, the angles opposite each other are the same.

Key ideas

  • At a point: 360 degrees in a full turn.
  • On a straight line: 180 degrees, half a turn.
  • Vertically opposite angles are equal.
Worked example 5.1.1
Angles a, b, c meet at a point and add to a whole turn. Angles 120, 85, 60 are known. Find the missing angle, in degrees.

Method. Take the sum of the known angles from 360.

  1. Angles at a point add up to 360 degrees. A full turn is 360 degrees.
    360
  2. Add the known angles. Add the angles you know.
    120 + 85 + 60 = 265
  3. Take the total from 360. The missing angle is what is left.
    360 - 265 = 95
  4. Write the answer.
    95

Check. 120 + 85 + 60 + 95 = 360. ✓

Watch out. Do not use 180 for angles at a point. A full turn is 360.

Worked example 5.1.2
Angle x and an angle of 35 degrees lie on a straight line. Find angle x.

Method. Take the known angle from 180.

  1. Angles on a straight line add up to 180 degrees. A straight line is half a turn.
    180
  2. Subtract the known angle. Take 35 from 180.
    180 - 35 = 145
  3. Write the answer.
    145

Check. 35 + 145 = 180. ✓

Watch out. Straight line: 180. Around a point: 360.

Worked example 5.1.3
Two straight lines cross. One of the angles is 65 degrees. What is the angle vertically opposite it?

Method. Vertically opposite angles are equal.

  1. Find the opposite angle. The angle opposite a 65 degree angle is the same size.
    65 degrees
  2. Check on a straight line. The other two angles are 180 - 65 = 115 degrees each, which is consistent.
    65 + 115 = 180
  3. Write the answer.
    65

Check. 65 + 115 = 180. ✓

Watch out

Watch out. A straight line is 180 degrees, not 360. Only a full turn at a point is 360.

Exam tip

Practice guide. Mark the known angles on the picture, then write the total next to the missing angle.

Exercise 5A  Practice: angles at a point, on a line and opposite

Non-calculator
1
FAngles p, q meet at a point and add to a whole turn. Angles 90, 140 are known. Find the missing angle, in degrees.
2
FAngles a, b, c, d meet at a point and add to a whole turn. Angles 45, 100, 75, 60 are known. Find the missing angle, in degrees.
3
FAngles x, y meet at a point and add to a whole turn. Angles 200, 50 are known. Find the missing angle, in degrees.
4
FAngle y and an angle of 72 degrees lie on a straight line. Find angle y.
5
FAngle x and an angle of 115 degrees lie on a straight line. Find angle x.
6
FTwo lines cross at a point. One angle is 40 degrees. Write the size of the angle vertically opposite it.
7
PSAngles a and b are on a straight line, and angle a is three times angle b. Find angle a, in degrees.
8
FWhich angle is a reflex angle? Choose one: 60 degrees, 90 degrees or 200 degrees.
9
FTick the statements that are true. Options: Angles on a straight line add up to 180 degrees | Angles at a point add up to 180 degrees | Vertically opposite angles are equal | Angles in a triangle add up to 360 degrees. Write the options you would tick, in the order given.
10
FIs an angle of 135 degrees acute, obtuse or reflex? Write one word.
135°
11
RExplain why the angles at a point add up to 360 degrees.
12
PSTwo straight lines cross. The angles around the crossing are a, b, a and b, where a = 62 degrees. Find b.
13
RAli says that two angles that sit opposite each other where two straight lines cross are always equal. Is he right? Write yes or no.
14
PSThree angles meet at a point. Two are 110 degrees and 95 degrees. Write the third, in degrees.

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings