Question

6. Three angles of a quadrilateral are equal and the fourth angle measures 75°. What is the measure
of each of the equal angles?
7. The angles of a quadrilateral are (5x)°, (3x + 10), (6x – 20)° and (x + 25)°. Find (i) the value of x
and (ii) the measure of each angle of the quadrilateral.
с
8. In a quadrilateral ABCD, it is being given that AB || DC.
ZA: ZD = 2:3 and ZB: 2C = 4:5.
Find the measure of each angle of quadrilateral ABCD.
Hint : 2x + 3x = 180 and 4y + 5y = 180.]
A
D
F
yo
In the adjoining figure, the sides BA and DC of a quadrilateral ABCD have been produced
to E and F respectively.
C
Prove that: a + b = x + y.
aº
[Hint : b° +/A = 180°, aº + 2C = 180°.
.a° +6° + ZA + ZC = 360°.
bº
But, xº + yº + ZA + ZC = 360°. [Angles of a quadrilateral]
E A
xº​

Answer 1

Three angles of a quadrilateral are equal and the fourth angle measures 75°. What is the measure

of each of the equal angles?

Answer:-

7. The angles of a quadrilateral are (5x)°, (3x + 10), (6x – 20)° and (x + 25)°. Find (i) the value of x

and (ii) the measure of each angle of the quadrilateral.

с

8. In a quadrilateral ABCD, it is being given that AB || DC.

ZA: ZD = 2:3 and ZB: 2C = 4:5.

Find the measure of each angle of quadrilateral ABCD.

Hint : 2x + 3x = 180 and 4y + 5y = 180.]

A

D

F

yo

In the adjoining figure, the sides BA and DC of a quadrilateral ABCD have been produced

to E and F respectively.

C

Prove that: a + b = x + y.

aº

[Hint : b° +/A = 180°, aº + 2C = 180°.

.a° +6° + ZA + ZC = 360°.

bº

But, xº + yº + ZA + ZC = 360°. [Angles of a quadrilateral]

E A

xº