Question

In the following figure of a ship, ABDH and CEFG are
two parallelograms. Find the value of x.

Answer 1

Answer:

Adjacent angles of parallelogram are supplementary and opposite angles are equal.

So, In parallelogram ABDH

∠A+∠B=180

o

∠D=∠A=180−∠B=180−130=50

o

Also, In parallelogram CEFG,

∠C=∠F=30

o

Hence , in ΔCDX

∠C+∠D+∠X=180

o

30+50+x=180

∠x=180−80=100

0

Answer 2

Step-by-step explanation:

Solution

We have, two parallelograms ABDH and CEFG.

In parallelogram ABDH,

∠

A

B

D

+

∠

B

D

H

=

180

∘

[

∵

adjacent angles of a parallelogram are supplementary]

⇒

∠

B

D

H

=

180

∘

−

130

∘

⇒

∠

B

D

H

=

50

∘

…

…

(

i

)

In parallelogram CEFG,

∠

G

C

E

=

∠

G

F

E

[

∵

Opposite angles are equal]

⇒

∠

G

C

E

=

30

∘

…

…

(

i

i

)

In

Δ

O

C

D

, by using angle sum property,

∠

O

C

D

+

∠

O

D

C

+

∠

C

O

D

=

180

∘

⇒

50∘+

30∘+x=

180∘

⇒x=180∘−80

100∘

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