Calculating angles II

Calculating angles II

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 with lines.
Calculate the angles in the following diagrams and give a reason for your answer.
Lines marked are parallel.

Question 1Change answer

a)  Calculate the size of the angle marked r and give a reason for your answer.
Calculating angles with lines diagram 1  [Not drawn to scale]
r =  º
Reason:

Question 1Change answer

b)  Calculate the size of the angles marked s and t and give a reason for each answer.

Calculating angles with lines diagram 2 [Not drawn to scale]
s =  º
Reason:
  
t =  º
Reason:

Question 1Change answer

c)

Calculating angles with lines diagram 3  [Not drawn to scale]
Are the lines marked m and n parallel? YesNo
Give a reason for your answer:
Task administration: 
This task can be completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
angles, parallel lines, alternate angles, co-interior angles, corresponding angles
Description of task: 
This task requires students to calculate the size of angles using their knowledge of angles and parallel lines: alternate angles, corresponding angles and co-interior angles. Understanding of adjacent angles on a straight line is also required.
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: 

 

Y11 (09/2001)

a)

  

60
Alternate angles are equal, parallel lines.

very easy
moderate

b)

i)

ii)

125
Corresponding angles are equal, parallel lines.
55 (or 180° - answer to b)i))
(Adjacent) angles on a straight line add to 180?are supplementary.

very easy
moderate
very easy
moderate

c)

  

No and
Because the co-interior angles do not add to 180?are not supplementary.

moderate

NOTE: Also accept other valid explanations.

Diagnostic and formative information: 
 

Common error

Likely miscalculation

Likely reason

c)

No and angles should be 90°.
Yes and angles are the same.

Co-interior angles are equal.

Assumes all angles to parallel lines meet at 90°.
Does not know that co-interior angles add to 180°, they are not equal.