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Angles in parallelograms and trapeziums
Look at parallelogram ABCD below. Cut out Z.ABC along the dotted line EF, and
place it next to ^FCD.
C,B
We see they form a straight llne.The sum of the two angles is 180°. ^ABC ar\d
ABCD are a pair of interior angles of the parallelogram. They are between the
parallel lines, AB and DC. Another pair of interior angles which are between the
parallel lines, >16 and DC, are ^>1DCand aDAB.
Look at trapezium PQRS. AQRS is cut off along the dotted line TU, and placed next
to APQU.
Q
Q □
The sum of the two angles is also 180°.
The sum of a pair of
interior angles in a APQR and AQRS are a pair of interior angles of the trapezium. They are between
quadrilateral is 180°. the parallel lines, PQ and SR. The other pair of interior angles, AQPS and APSR,
also add up to 180°.
The sum of all interior
angles in a quadrilateral Look the square and the rectangle in Example 2. The sum of each pair of interior
= 180° X 2 = 360°. angles is 180°.
Example 3
0 AeCD is a parallelogram ./D/46= 124°.
Find 124°
a) zlx, b) ABCD.
A BAD
Solution
another
a) Zx+124° = 180° Interior angles between the parallel lines/4D and 6C.
^x= 180°- 124°
= 56°
b) 56° + ABCD = 180° Interior angles between the parallel lines 46and DC.
^6CD= 180°-56°
= 124°
Angles and Their Properties
