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Example 14: The angles of a quadrilateral are (3x + 2)°, (x – 3)°, (2x + 1)° and 2(2x + 5)°, respectively.
Find the value of x and the measure of each angle.

Solution: Using the angle sum property of a quadrilateral, we get
(3x + 2)° + (x – 3)° + (2x + 1)° + 2(2x + 5)° = 360°

3x° + 2° + x° – 3° + 2x° + 1° + 4x° + 10° = 360°
Maths Talk
10x° + 10° = 360° According to the angle sum
10x° = 360° – 10° property, the sum of interior angles of
a convex quadrilateral is 360°. Can a
10x° = 350° concave quadrilateral hold the same

350° property? Discuss with the classmate.
x° =
10 Give your reason, if it hold the same.
⇒ x = 35
\ (3x + 2)° = (3 × 35 + 2)° = 107°;

(x – 3)° = (35 – 3)° = 32°;
(2x + 1)° = (2 × 35 + 1)° = 71°;

and 2(2x + 5)° = 2 × (2 × 35 + 5)° = 150°
Thus, the four angles of the quadrilateral are 32°, 71°, 107° and 150° respectively.

Kinds of Quadrilaterals

There are different types of quadrilaterals, depending
on the nature of their sides and angles.
Quadrilateral
Quadrilaterals are basically classified into three
categories: Trapeziums, kites and parallelograms.

Trapezium
Trapezium Parallelogram Kite
If a quadrilateral has one pair of parallel sides, then
it is called a trapezium.

The figure given below is a trapezium ABCD, where Isosceles
AB is parallel to DC, that is AB || DC. Trapezium Rectangle Rhombus

D C

Square

A B

Note: The arrow marks in same direction indicate parallel lines.

In the trapezium ABCD, if we take AD as a transversal, then the sum of the two angles on the same
side AD is equal to 180°, that is ∠A + ∠D = 180°.

Similarly, if we take BC as a transversal, then ∠B + ∠C = 180°.

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