The idea in brief. Every corner of a rectangle and of a square is a right angle, so the parts a line cuts a corner into add up to 90 degrees, not 180; and a side is read off the marks, since sides hatched alike are equal and the side opposite is the whole of what faces it.
Lesson video, with the working
Angles in rectangles and squares
3 min 13 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABCD is a rectangle, lettered clockwise from the top left. The line BP is drawn from B to a point P on DC. ∠ABP = 31°. Find ∠PBC.
∠ABC = 90°
∠PBC = 90° − 31°
= 59°
Ans: 59°
Example 1
EFGH is a rectangle, lettered clockwise from the top left. Two lines HJ and HK are drawn from H to the points J and K on EF. ∠EHJ = 26° and ∠KHG = 18°. Find ∠JHK.
∠EHG = 90°
∠JHK = 90° − 26° − 18°
= 46°
Ans: 46°
How to solve it
Find the corner containing the given angle and the unknown angle. Angle ABC is a right angle, 90 degrees.
Use the middle letter to find the vertex. The 31-degree angle is between BA and BP.
Subtract the given part: angle PBC is 90 degrees minus 31 degrees, which is 59 degrees.
When both given parts share the right angle, subtract both.
Angle JHK is 90 degrees minus 26 degrees minus 18 degrees, which is 46 degrees.
Name the right angle first. Subtract every given part inside it.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its full working.
Question 1 of 19 · Basic · free to tryWXYZ is a rectangle, lettered clockwise from the top left. The line MN cuts…WXYZ is a rectangle, lettered…
WXYZ is a rectangle, lettered clockwise from the top left. The line MN cuts it into two smaller rectangles, with M on WX and N on ZY. The hatch marks show that WM and MX are equal in length. MX = 7 cm and XY = 4 cm. Find the length of ZY.
ZY = WX = 14 cm, because opposite sides of a rectangle are equal.
Answer: 14 cm
For parents
How can I explain rectangle and square properties to my child?
Your child learns to recognise a rectangle or square from what is known about its sides and corners, even when the figure is turned.
What your child learns here
Your child learns to recognise a rectangle or square from what is known about its sides and corners, even when the figure is turned. The Primary 4 syllabus names their properties and explicitly excludes diagonal properties. Here, equal lengths, parallel sides and right angles provide the reasons for a conclusion, so a figure's appearance supports the explanation without replacing the stated information.
Recognise that a rectangle has four right angles and two pairs of equal opposite sides, with opposite sides parallel.
Use a square's four equal sides and four right angles together; equal sides on their own do not establish that a figure is a square.
Read matching side marks and given lengths to identify which sides have equal measures, including when the figure is rotated.
Use the 90° corner of a stated rectangle or square to find an unknown part when that corner is divided into smaller angles.
Does the answer make sense?
If a line splits one rectangle corner into two adjacent angles, the two measurements must add to 90°. After finding the unknown part, your child can add it to the given part and confirm that the original right angle is recovered.
How to practise these questions
Basic work uses equal-side marks to recover a rectangle's length. The Intermediate questions develop parallel and perpendicular relationships, the link between squares and rectangles, missing side totals and angles within a right-angle corner. Challenge questions connect a difference between angle parts, figures meeting at a vertex or a folded corner to the required angle. Choose a question about side properties before moving to the angle problems if your child needs a steadier entry. For each angle calculation, ask which stated corner or fold supplies the relationship being used. Check the written reasoning as well as the final number, particularly when several angle names share the same vertex or a fold carries an angle to another position. Its multiple-choice Basic questions show a lettered rectangle or square and ask which statement about its sides, its parallel and perpendicular lines or its angles is true.
Questions parents ask
Is a square also a rectangle? Yes. A square meets the rectangle conditions of four right angles and equal opposite sides, and also has all four sides equal. When a question asks for the most specific name, square supplies that extra information. Your child can explain the relationship by listing the properties that both figures share before naming the additional equal-side condition.
Can my child decide from the way a figure looks? Appearance can suggest what to investigate, but the written description, measurements and marks establish what is known. A tilted square is still a square, while a roughly drawn corner may not look exactly square on a screen. Encourage your child to point to a stated property or a mark when explaining a missing length or angle.
Does Primary 4 require rules about rectangle diagonals? No. The MOE outcome for rectangle and square properties specifically excludes diagonal properties. Your child can work with side equality, parallel lines and right angles without learning additional diagonal rules for this page. If a line is drawn across a corner, use only the angle information given rather than assuming that the line halves the corner.
