Angles and Shape: Practice Set 2
Angles and Shape: Practice Set 2 is a second practice round for 11+ angle work, revisiting angle facts on a line, at a point and in triangles before pushing into quadrilaterals, isosceles triangles and angles given in a ratio.
Method
- Remember the core angle facts: angles on a straight line add up to 180 degrees, angles around a point add up to 360 degrees, and angles in a triangle add up to 180 degrees.
- Angles in a quadrilateral add up to 360 degrees, so if three angles are known, the fourth can be found by subtracting their sum from 360.
- When two straight lines cross, the vertically opposite angles are equal to each other.
- In an isosceles triangle, the two base angles are equal, so once one base angle is known, the other is the same and the third angle can be found using the angle sum of a triangle.
- Build up a diagram step by step, labelling every angle you find so that later steps can reuse earlier results.
- Check that all the angles you have found for one shape or one point add back up to the correct total for that fact.
Worked example
In triangle ABC, angle A is 48 degrees and angle B is 65 degrees. Calculate angle C.
- Add the two known angles: 48 + 65 = 113 degrees.
- Subtract this total from 180 degrees, since angles in a triangle add up to 180 degrees: 180 - 113 = 67 degrees.
- Check the three angles add back up to 180 degrees: 48 + 65 + 67 = 180, which confirms the answer.
- Final answer: 67 degrees.
Practice questions
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Q1Two angles on a straight line are 112 degrees and x. Find x.Show answer
Answer: 68 degrees
Q2Four angles around a point are 90, 85, 100 and y degrees. Find y.Show answer
Answer: 85 degrees
Q3A triangle has two angles of 55 degrees each. Find the third angle.Show answer
Answer: 70 degrees
Q4A quadrilateral has three angles of 80, 95 and 110 degrees. Find the fourth angle.Show answer
Answer: 75 degrees
Q5Two straight lines cross, forming an angle of 37 degrees on one side. Find the vertically opposite angle.Show answer
Answer: 37 degrees
Q6An isosceles triangle has a base angle of 72 degrees. Find the other two angles.Show answer
Answer: 72 degrees and 36 degrees
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A straight line is divided into three angles: 42 degrees, 65 degrees and z. Calculate the value of z.
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In an isosceles triangle, the angle at the apex (the odd one out) is 34 degrees. Calculate the size of each base angle.
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A quadrilateral has angles in the ratio 2 : 3 : 4 : 6. Calculate the size of the largest angle.
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Free printable worksheet
Want more practice on paper? Download the angles and shape: practice set 2 worksheet pack - 21 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 24 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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