iGCSE Mathematics (0580) - C4.1 Geometrical terms- Exam Style Questions Paper 3- New Syllabus

Question

(a) Shape A is a quadrilateral with only one pair of parallel lines.

Write down the mathematical name of shape A.

(b) Shape B is a quadrilateral with

two pairs of parallel lines
all four sides equal
no right angles.

Write down the mathematical name of shape B.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• C4.1 Geometrical terms

▶️ Answer/Explanation

(a)
A quadrilateral with exactly one pair of parallel lines is uniquely defined as a trapezium.
✅ Answer: trapezium

(b)
A quadrilateral with all four sides equal and two pairs of parallel lines is either a square or a rhombus. Since it has no right angles, it must be a rhombus.
✅ Answer: rhombus

Question

(a)

Write down the mathematical name for this type of angle.

(b) ABC is a triangle.

Lily says $x$ is $34$.
Give a geometrical reason why Lily is not correct.

(c)

ABCD is a quadrilateral. DCE is a straight line.
The interior angles are $48^\circ$, $126^\circ$, $75^\circ$, and angle BCD. Angle BCE is labeled $x^\circ$.
Calculate the value of $x$.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• C4.1 Geometrical terms (a)

• C4.6 Angles (b,c)

▶️ Answer/Explanation

(a)
An angle greater than $180^\circ$ and less than $360^\circ$ is a reflex angle.
✅ Answer: reflex

(b)
Sum the angles: $102 + 54 + 34 = 190^\circ$. This exceeds the sum of angles in a triangle.
✅ Answer: Angles in a triangle must add up to $180^\circ$.

(c)
First, find the interior angle BCD of the quadrilateral. The sum of angles in a quadrilateral is $360^\circ$.
$\text{Angle BCD} = 360^\circ – (126^\circ + 48^\circ + 75^\circ) = 360^\circ – 249^\circ = 111^\circ$
Since DCE is a straight line, angles on a straight line add to $180^\circ$.
$x = 180^\circ – 111^\circ = 69^\circ$
✅ Answer: $x = 69$

iGCSE Mathematics (0580) - C4.1 Geometrical terms- Exam Style Questions Paper 3- New Syllabus

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