Question

ABCD is a parallelogram in which ∠DAB = 70° and ∠CBD=55°. Find ∠CDB and ∠ADB.​

Answer 1

Question :

ABCD is a parallelogram in which ∠DAB = 70° and ∠CBD=55°. Find ∠CDB and ∠ADB.

Solution :

▪Given : ABCD is a parallelogram ∠DAB = 70° and ∠CBD=55°.

▪To Find : ∠CDB and ∠ADB.

▪Solution :-

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Properties of parallelogram :

1 .Opposite angles of parallelogram Are Equal .

2. Alternate Interiors Angle of parallelogram are Equal .

3. Sum of All angles of parallelogram is 360°

4. Two opposite lines are parallel and the Never intersect each other .

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● So , Angle opposite to ∠DAB is ∠CBD

so According to Property 1 ,

=》∠DAB = ∠DCB = 70°

Now , We know that ,

☆ Sum of all Angles of a triangle is 180°

So , In Triangle DBC ,

=》 ∠DCB + ∠CBD + ∠CDB = 180°

=》 70° + 55° + ∠CDB = 180°

=》 125° + ∠CDB = 180 °

=》 ∠CDB = 180° - 125°

=》 ∠CDB = 55°

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Now For ∠ADB ,

Using property 2 ,

∠CBD = ∠ADB = 55°

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Note :

♢ Check the attachment for the diagram .

Answer :

The value of ∠CDB is 55° and the value of ∠ADB is 55° .