Question

C 27 (i) Calculate the measures of x and y in the parallelogram ABCD 2 А B 429 56° 100° y 5 80 100 х - D​

Answer 1

Answer:

Step-by-step explanation:

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  

∘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  

∘