Question

AD
11. The figure shows a kite ABCD where AB =AD and
BC = CD and the diagonals AC and BD intersect
at E

Find
(1) ABD
(ii) CBD


(please give correct and accurate step by step solution:)​

Answer 1

To find -

Find Angle ABD and and CBD.

Solution -

See the attached figure of a kite .

Here , according to the criterias -

AD = AB

&

CB = CD .

Now, first let us see ∆ ADB .

Here ,

AB = AD & Angle DAE = 25°

Now ,

Angle DAE = Angle EAB = 25°

So, angle DAB = 50°

Now , we know that in a triangle , the sum of all the angles is 180°

=> Angle DAB + Angle ADE + Angle ABE = 180°

=> 50° + Angle ADE + Angle ABE = 180°

=> 50° + 2 Angle ADE = 180°

=> 2 Angle ADE = 130°

=> Angle ADE = 65° .

But , angle ABE = Angle ADE .

Thus ,

Angle ABE = Angle ADE = 65°

{ Note - Angle ABD and angle ABE are the same angle . }

Now, first let us see ∆ BCD .

Here ,

BC = CD & Angle DCE = 44°

Now ,

Angle DCE = Angle ECB = 44°

So, angle DCB = 88°

Now , we know that in a triangle , the sum of all the angles is 180°

=> Angle DCB + Angle DBC + Angle BDC = 180°

=> 88° + Angle DBC + Angle BDC = 180°

=> 88° + 2 Angle DBC = 180°

=> 2 Angle DBC = 92°

=> Angle DBC = 46°

But , angle DBC = Angle BDC .

Thus ,

Angle DBC = Angle BDC = 46°

This is the required answer .

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