Question

9. In the given figure, both ABCD and PQRS are
parallelograms. Find the value of x.
S С
D
R
[
130°
70°
х
SA
D
B
Р
10. Find x and y in following parallelograms.
R
OP
36​

Answer 1

Answer:

Ans 9 ) Given: Three angles of a quadrilateral are 75°, 90° and 75°.

Let the fourth angle be x.

Using angle sum property of quadrilateral,

75°+90°+75°+x=360°⇒240°+x=360°

⇒x=360°-240°⇒x=120°

So, the measure of the fourth angle is 120°.

Step-by-step explanation:

Ans 10 ) Since ABCD is a parallelogram, AB∥DC and AD∥BC

Now, AB∥DC and transversal BD intersects them.

∴∠ABD=∠BDC since alternate angles are equal.

⇒10x=60

∘

⇒x=

10

60

∘

=6

∘

And, AD∥BC and transversal BD intersects them.

∴∠DBC=∠ADB

⇒4y=28

∘

⇒y=

4

28

∘

=7

∘