Page 18 - Cambridge IGCSE Mathematics Core and Extended

Example 12
Find the value of x in the quadrilateral.
x 108°
68°
71°
Solution
The sum of the angles of a
x + 108° + 68° + 71° = 360°
quadrilateral is 360°.
x = 360° – 108° – 68° – 71°
= 113°
F. Problem-solving
Example 13 M

In the diagram, JKLN is a quadrilateral and 70° N
L
KLM is a straight line. Find the value of y. 120°

y
K J
Solution
Sum of adjacent angles
70° + /KLN = 180° on a straight line is 180º.
/KLN = 180° – 70°
= 110°
Sum of angles of a
y + 90° + 120° + 110° = 360°
quadrilateral is 360º.
y = 360° – 90° – 120° – 110°
= 40°
Test Yourself 11.4

1. For each of the following quadrilaterals, (e) Quadrilateral KLMN with KL = 7.2 cm,
determine whether it has line(s) of symmetry. LM = 5.6 cm, /LKN = 60°, /KLM = 70°
Draw the line(s) of symmetry for the and /LMN = 100°.
quadrilaterals that have lines of symmetry. (f) Quadrilateral PQRS with PQ = 8 cm,
(a) (b) PS = 7 cm, QR = 5.4 cm, /QPS = 70°
and /PQR = 120°.

3. (a) Name the quadrilaterals that have
(c) (d)
equal interior angles.
(b) Name the quadrilaterals that have four
sides of equal length.
(c) Quadrilateral A has equal opposite
2. Draw each of the following quadrilaterals
using a protractor and a ruler. angles and its opposite sides are
(a) A square with sides 4.2 cm each. parallel and of equal length. State the
(b) A rectangle with adjacent sides 5.6 cm type of quadrilateral A.
and 4.5 cm respectively. (d) Which quadrilateral has only one pair
(c) Parallelogram ABCD with AB = 6.8 cm, of sides that are parallel?
BC = 4.6 cm, /ABC = 70° and (e) Name two common geometric properties
/BCD = 110°. of a rectangle and a parallelogram.
(d) Trapezium EFGH with two
(f) List the quadrilaterals that have their
parallel sides, EF = 6 cm and
diagonals which are equal and bisect
GH = 4 cm respectively, EH = 5.2 cm
each other.
and /FEH = /EHG = 90°.
158 Cambridge IGCSE Mathematics

14/07/2022 10:15 AM
DA1501_pg 147 to 161.indd 158
DA1501_pg 147 to 161.indd 158 14/07/2022 10:15 AM