# Primary Math

## Primary Math: Let’s Learn About Angles! (PSLE 2021 Q7 & PSLE 2021 Q13)

Did you know: the topic of Angles & Geometry takes up around 20% of the Primary Math/ PSLE Paper? They are the most-tested topics after Numbers, Measurements, and Ratio and Percentage.

By acing these essential Math topics, that’s like having a super-sized slice of exam success pie!

Ready to uncover the secret ingredients to PSLE Math success? Let’s dive in together and learn how to conquer those geometric challenges!

## Is your Primary child familiar with these Math Properties of Angles & Geometrical Shapes?

### Angle Properties

• Right Angles (90°)

• Acute Angles (Less than 90°)

• Obtuse Angles (More than 90°)

• Angles on a straight line adds up to 180°

• Vertically opposite angles [x]

• Alternate angles [z]

• Square

• All sides are equal
• Two pairs of parallel lines
• All angles add up to 360°
• Rectangle

• Opposite sides are equal
• Two pairs of parallel lines
• All angles add up to 360°
• Trapezium

• Only 1 pair of parallel lines
• All angles add up to 360°

### Different Types of Triangles

• Equilateral Triangle
• All sides are equal
• All angles are equal
• All angles add up to 180°
• Isosceles Triangle
• Only 2 sides are equal
• Only 2 angles are equal
• All angles add up to 180°
• Scalene Triangle
• None of the sides are equal
• None of the angles are equal
• All angles add up to 180°
• Right – Angle Triangle
• Only 2 angles are equal
• There is 1 right angle
• All angles add up to 180°
• Right – Angle Isosceles Triangle

• Only 2 angles are equal
• There is 1 right angle
• All angles add up to 180°

## How to utilise the geometric properties to tackle these challenging PSLE Math Angles Questions

### ABCD is a rhombus and EFG is an equilateral triangle. DGH is a straight line. Find ∠y.

#### Step 1:

Read the Math Question and identity the concept of this math question by looking at the keywords “Rhombus, Equilateral triangle and straight lines”. The keywords will tell you that this is a Geometry question.

#### Step 2:

Since it’s a Geometry question, ask yourself what the properties of the rhombus are, and this will be the first clue that is given to you in the question. At Bluetree, we use “Read and Write” for all our math lesson. Since opposite angles of a Rhombus are equal, we can deduce that ∠ABC = ∠ADC = 102°.

#### Step 3:

The second clue that is given to you in the question would be the keyword “equilateral triangle”. Ask yourself again what the properties of an equilateral triangle are. All the angles of an equilateral triangle are equal hence ∠EFG = ∠EGF = FEG = 60°.

#### Step 4:

The third clue that is given to you in the question would be DGH is a straight line. If you are familiar with the property of angles on a straight line adds up to 180°, from this clue, we can find ∠DGX by taking 180° – 96° – 60° = 24°.

#### Step 5:

Now that you had found all the possible angles by using the keywords that were presented to you in the question, look at the diagram and look for more clues.

By looking at the diagram, you will then be able to find ∠GDX by using the property angles at a point adds up to 360° by taking 360° – 155° – 102° = 103°

#### Step 6:

We then move on to find ∠DXG by taking 180° – 103° – 24° = 53° as sum of angles in a triangle adds up to 180°.

#### Step 7:

From the diagram, student will be able to see the letter X and this shows that ∠CXE = ∠DXG = 53° as they are vertically opposite angles hence they are equal.

#### Step 8:

Lastly to find ∠y, the sum of angles in a triangle adds up to 180°. Hence, 180° – 60° – 53° = 67° (Ans)

If you prefer to watch the video solution, you may watch it here:

### a) Find ∠BCE. [1 mark] b) Find ∠AEC. [2 marks]

#### Step 1:

Read the Math Question and identity the concept of this math question by looking at the keywords “trapezium, parallel, AE = EB and straight lines”. The keywords will tell you that this is a Geometry question.

#### Step 2:

To solve part a, ∠BCE = 180° – 28° – 94° = 58° (Ans) as sum of angles in a triangle adds up to 180o.

#### Step 3:

The first clue that is given to you in the question would be the keyword “ABCD is a trapezium with AB parallel to DC”. Ask yourself again what the properties of a trapezium and what does the angles of the parallel lines adds up to? We can use the property where interior angles adds up to 180° and we can find out that ∠BCD = 180° – 58° – 53° = 69°.

#### Step 4:

Based on the diagram, since ∠EBC = 94o and ∠BCD = 69°, we can find ∠ABE = 94° – 69° = 25°.

#### Step 5:

The second clue that is given to you in the question would be the keyword “AE = EB”. This clue shows that triangle ABE is an isosceles triangle, hence ∠ABE = ∠EAB = 25°.

#### Step 6:

Now that you had found all the possible angles by using the keywords that were presented to you in the question, look at the diagram and look for more clues.

By looking at the diagram, you will then be able to find ∠AEC by using the property sum of angles in a triangle adds up to 180° by taking 180° – 25° – 25° – 28° = 102°. (Ans)

### c) Circle the words that describe AFCD in the statement:

From the question, AF is parallel to DC. We cannot assume that AD is parallel to FC as the question did not state that. With only 1 pair of parallel line, AFCD can only be a trapezium and not a parallelogram as parallelogram must have 2 sets of parallel lines. Hence, this goes back to how familiar you are with the properties of angles and figures to solve Geometry questions.

Since AF (is / is not) parallel to DC and AD (is / is not) parallel to FC, AFCD is a (parallelogram / trapezium).

## 4 Common mistakes that students are making when tackling Primary Math Angles (Geometry) Questions

There are 4 important things to take note when answering angles question:

1. Angle referencing for each step is important.
2. Renaming of angles.
3. Write each step clearly.
4. Indicate degree symbol.

Read Also: Problem? WITH MATH PROBLEM SUMS?