Year 7 angles and parallel lines test answers to download as PDF

These Year 7 angles and parallel lines test answers give the worked solutions and the marks for every question of the angles and parallel lines test. The test is marked out of 20, so you can work out your score.

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Answer to Question 1 (4 marks)
1. Angles on a straight line add up to 180°, so \(3x+2x+20=180\) (1 mark). Collect the x terms: \(5x+20=180\). Subtract 20: \(5x=160\). Divide by 5: \(x=32\) (1 mark).
2. Substitute \(x=32\) into each angle. The first is \(3\times32=96°\) and the second is \(2\times32+20=84°\). The largest angle is 96°. (1 mark)
3. The reason is: angles on a straight line add up to 180°. The full wording is needed for the mark. (1 mark)
Check: \(96+84=180\), so the two angles really do fit together on a straight line.
Answer to Question 2 (4 marks)
1. The three angles of any triangle add up to 180°. Subtract the two known angles: \(180-47-85=\)48°. (1 mark)
2. In an isosceles triangle the two base angles are equal. Take the apex away from 180°: \(180-54=126°\), then share it equally between the two base angles: \(126\div2=\)63°. (1 mark)
3. A quadrilateral splits into two triangles, so its angles add up to 360° (1 mark for using 360°). The three known angles total \(88+102+79=269°\), so the fourth angle is \(360-269=\)91° (1 mark).
Check (b): \(63+63+54=180\). Check (c): \(269+91=360\).
Answer to Question 3 (4 marks)
1. The angle x and the 72° angle sit next to each other on the same straight line, so \(x=180-72=\)108°. Reason: angles on a straight line add up to 180°. (1 mark for value and reason)
2. The angle y is in the same position at the second crossing as the 72° angle is at the first crossing, so \(y=72°\). Reason: corresponding angles on parallel lines are equal. (1 mark)
3. The angle z is vertically opposite the angle that corresponds to x, so \(z=108°\) (1 mark). Both reasons must be stated: corresponding angles are equal and vertically opposite angles are equal (1 mark).
Check: \(y+z=72+108=180\), which is correct because y and z lie on one straight line at the second crossing.
Answer to Question 4 (4 marks)
1. The roof is isosceles, so both base angles are 35°. Together they make \(2\times35=70°\). The angles of a triangle add up to 180°, so the apex angle is \(180-70=\)110°. (1 mark)
2. The vertical post joins the apex to the middle of the base, so it is the line of symmetry and cuts the apex angle in half: \(110\div2=\)55° on each side (1 mark). Check with one of the small right-angled triangles: \(90+35+55=180\) (1 mark).
3. The steepness of a roof is measured by its angle with the horizontal. Since \(40°\gt35°\), the 40° roof is steeper. (1 mark)
Answer to Question 5 (4 marks)
1. A regular octagon has 8 equal interior angles, so share the total equally: \(1080\div8=\)135°. (1 mark)
2. At each vertex the interior and exterior angles lie on a straight line, so together they make 180°. Each exterior angle is \(180-135=\)45°. (1 mark)
3. The exterior angles of any polygon add up to 360° (1 mark). For a regular polygon they are all equal, so the number of sides is \(360\div40=\)9. The polygon is a nonagon (1 mark).
Check (b): \(8\times45=360\), as it should be. Check (c): each interior angle of the nonagon is \(180-40=140°\), and \(9\times140=1260=(9-2)\times180\).

Total : 20 marks

How to use these Year 7 angles and parallel lines test answers

First, sit the test under timed conditions before you read anything here. Then mark each answer and give yourself the marks shown, including method marks. When you lose marks, read the worked solution and find the step you missed. After that, revise the angles and parallel lines lesson and redo the worksheet.

Also, the Year 7 angles and parallel lines test answers are available as a PDF, so a teacher can mark printed tests quickly. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.