Sum of the angles

Sum of the angles

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about angle properties.
 Look at the diagram below and answer the questions.
sum-of-angles.png
                                                                                     [Not drawn to scale]

Question 2Change answer

a)  What is the sum, in degrees, of the angles marked 'r' and 's'?  °

Question 2Change answer

b)  i)  What is the size, in degrees, of the angle marked 'p'?  °
ii) Justify your answer.
Task administration: 
This task can be completed with pencil and paper or online (with some auto-marking).
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
angles, circles, tangents, radius, quadrilaterals
Description of task: 
Students use their knowledge of the angle between a tangent and radius property and the sum of the angles in a quadrilateral to work out unknown angles in a diagram and explain their workings.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (09/1998)
a)   180 difficult
b) i)
ii)		 130
Because the angles of a quadrilateral sum to 360° (or an equation written out correctly showing 360° in it).		 difficult
difficult
Diagnostic and formative information: 
  Common error Likely reason
a) 90 Size of r (or s) rather than r + s