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Now, substitute the value of x in the given angles,
we get Think and Answer

(3x + 5)° = (3 × 14 + 5)° In a parallelogram, one external
angle is given. Can you find out all the four
= (42 + 5)° = 47° angles of the parallelogram?
And (61 – x)° = (61 – 14)° = 47°

Both the angles are 47° as the opposite angles are equal.
Now, we have, ∠A + ∠B = 180° (Adjacent angles of a ||gm are supplementary)

47° + ∠B = 180°
∠B = 180° – 47° = 133°

The fourth angle will also be 133°, i.e., ∠D = 133° as the opposite angles are equal.
Hence, the four angles of the given parallelogram are 47°, 47°, 133° and 133°.

Practice Time 3C

1. Find the value of unknown angles in the following figures.

(a) A B (b) P (c) Q
94° P m
x
74° 107°
Q
x
81° 57°
D C 69° 73° 62° 54°
S R S R
(d) T 75° I (e) M N (f) X Y
y x y 38° z

110° 75° 34° y
E P O x Z
105° M W
2. A quadrilateral has three acute angles each of measure 80°. What is the measure of the fourth angle?
3. Two angles of a quadrilateral are of measure 50˚ and the other two angles are equal. What is the
measure of each of the equal angles?
4. If the four angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8, find the measures of each angle.

5. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of the smallest angle.
6. ABCD is a parallelogram with one angle as 75°. Find the other three angles of the given parallelogram.
7. The perimeter of a parallelogram is 150 cm. One of its side is greater than the other by 25 cm. Find
the sides of the parallelogram.
8. What value of ‘b’ will make the given quadrilateral a parallelogram? 5b – 7
3b + 6
9. In a parallelogram PQRS, diagonals PR and QS intersect at O and
PR = 12.8 cm and QS = 7.6 cm. Find the measure of OR and OS.
10. The angles A, B, C and D of a quadrilateral ABCD are in ratio 1 : 3 : 7 : 9.

(a) Find the measure of each angle. (b) Is ABCD a trapezium? Why?
(c) Is ABCD a parallelogram? Why?

71 Quadrilaterals