New
New
Year 8

Securing understanding of angles from KS2

I can confidently state the sums of the angles around a point and on a straight line.

New
New
Year 8

Securing understanding of angles from KS2

I can confidently state the sums of the angles around a point and on a straight line.

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Lesson details

Key learning points

  1. The sum of angles at a point can be used to find missing angles.
  2. The angle sum of a straight line can be used to find missing angles.
  3. Vertically opposite angles can be used to find missing angles.
  4. The size of missing angles can be justified by using known facts.

Common misconception

Angles on a straight line sum to 180°

Angles on a straight line only sum to 180° if all of those angles share a common vertex. Show two angles "on a line" at different points.

Keywords

  • Vertical angles - Vertical angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.

  • Vertex - A vertex is the point where two or more line segments meet. The plural is vertices.

  • Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

  • Supplementary angles - Supplementary angles are a pair of angles that sum to 180°.

  • Conjugate angles - Conjugate angles are a pair of angles that sum to 360°.

When applying angle facts to reason the value of unknown angles, all diagrams must be assumed as "not drawn to scale". Finding the size of an angle using a protractor is not a valid method.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Complete the sentence: The two angles of 44° and 136° are ____________ with each other.
right angled
complementary
Correct answer: supplementary
conjugate
opposite
Q2.
The size of angle $$a$$ is measured accurately. Which of these statements could be accurate for angle $$a$$?
An image in a quiz
angle $$a$$ is acute
Correct answer: angle $$a$$ is obtuse
angle $$a$$ is reflex
angle $$a$$ is 36°
Correct answer: angle $$a$$ is 144°
Q3.
Match the angle name to its size.
Correct Answer:acute,11.7°

11.7°

Correct Answer:right angle,90°

90°

Correct Answer:obtuse,117°

117°

Correct Answer:reflex,217°

217°

Correct Answer:one full turn,360°

360°

Q4.
Match the pairs of angles to their description.
Correct Answer:30° and 60°,lie on a right angle

lie on a right angle

Correct Answer:45° and 135°,supplementary angles

supplementary angles

Correct Answer:120° and 240°,conjugate angles

conjugate angles

Correct Answer:120° and 140°,two random angles

two random angles

Q5.
Which of these statements about this diagram are accurate?
An image in a quiz
Angles $$b$$° and 172° are supplementary angles.
Correct answer: Angles $$b$$° and 172° are conjugate angles.
Correct answer: $$b$$ = 188.
$$b$$ is a minor angle.
Correct answer: $$b$$ is a major angle.
Q6.
QR is a line segment. Find the value of $$c+d+g+h$$.
An image in a quiz
Correct Answer: 260, 260°, 260 degrees, 260degrees

6 Questions

Q1.
TU is a line segment. Angle $$a$$° = °.
An image in a quiz
Correct Answer: 40, 40°, 40 degrees, 40degrees
Q2.
These three angles lie around a point on a full turn. Angle $$b$$° is °.
An image in a quiz
Correct Answer: 100, 100°, 100 degrees, 100degrees
Q3.
This diagram shows four angles around two line segments that meet at an intersection. Which of these statements are correct for angle $$c$$°?
An image in a quiz
Correct answer: Angle $$c$$° and 59° are supplementary.
Angle $$c$$° and 59° are vertically opposite.
Angle $$c$$° is 59°.
Correct answer: Angle $$c$$° is 121°.
Angle $$c$$°is 301°.
Q4.
This diagram shows four angles around two line segments that meet at an intersection. Which of these statements are correct for angle $$d$$?
An image in a quiz
Angle $$d$$° and 59° are supplementary.
Correct answer: Angle $$d$$° and 59° are vertically opposite.
Correct answer: Angle $$d$$° is 59°.
Angle $$d$$° is 121°.
Angle $$d$$° is 301°.
Q5.
PQ and RS are straight line segments. Angle $$e$$° = °.
An image in a quiz
Correct Answer: 78, 78°, 78 degrees, 78degrees
Q6.
PQ and RS are straight line segments. Match each angle to its size.
An image in a quiz
Correct Answer:$$f$$°,128°

128°

Correct Answer:$$g$$°,52°

52°

Correct Answer:$$h$$°,38°

38°

Correct Answer:right angle,90°

90°

Correct Answer:not an angle on the diagram,32°

32°