Question

in the given figure ABCD is a parallelogram in which ∆BCD =70°and∆ADB=60°.find ∆ABD and ∆CBD​

Answer 1

Answer:

your answer is in the image

Answer 2

Answer :

The measure of the angles :-

➔ ∠ABD = 50°

➔ ∠CBD = 60°

Step-by-step explanation :-

To Find:-

• ∠ABD
• ∠CBD

Solution:-

Given that,

• ABCD is a parallelogram
• ∠BCD = 70°
• ∠ADB = 60°

ACCORDING THE QUESTION,

• First let's find out the ∠ABD,

As we know that, by a properties of parallelogram,

• Opposite angles of parallelogram are equal,

∴ ∠DAB = ∠BCD = 70°

• Each diagonal bisects the parallelogram, divides into two congruent triangles,

∴ ∠ADB + ∠DAB + ∠ABD

So, therefore by angle sum property of triangle we can find out ∠ABD,

➦ 60° + 70° + ∠ABD = 180°

➦ 60 + 70 + ∠ABD = 180

➦ ∠ABD = 180 - 70 - 60

➦ ∠ABD = 180 - 130

➦ ∠ABD = 50°

The measure of ∠ABD is 50°.

Now, let's find out ∠CBD,

As we know that, by the property of parallelogram,

• Adjacent angles of parallelogram are supplementary ( 180° ),

∴ ∠BCD + ( ∠CBD + ∠ABD ) = 180°

➦ 70° + ( ∠CBD + 50° ) = 180°

➦ ∠CBD = 180 - 70 - 50

➦ ∠CBD = 180 - 120

➦ ∠CBD = 60°

The measure of ∠CBD is 60°.