Question

In the adjoining figure, ABCD is a kite. find <ABD , <ADC, <BAD.​

Answer 1

Answer :

<ABD = 28°

<ADC = 70°

<BAD = 110°

Answer 2

Answer:

Step-by-step explanation:

Concept:

The concept of geometry will be used to solve this question.

Given:

According to the picture, $ABCD$ is a kite.Here $\angle C=55^{\circ }$ and $\angle B=28^{\circ }$.

To Find:

We need to findout the values of the following angles which are $\angle ABD , \angle ADC, \angle BAD$ .

Solution:

Consider the middle point of the kite is $M$ .

Refer the following picture.

According to the picture, the value of $\angle DMC=90^{\circ }$ and the value of $\angle DCM=55^{\circ }$ .

Then the value of $\angle MDC=180^{\circ }-(55^{\circ }+90^{\circ })=35^{\circ }$.

The side $AB=BC$ according to the picture.

So $\angle ABD=\angle DBC=28^{\circ }$.

In the picture, $AD=DC$.

So $\angle ADC$ will be the double of $\angle MDC$.

The the value of $\angle ADC$ is $2 \times \angle MDC=2 \times 35=70$ .

According to the figure, $\angle MCD=\angle MAD=55^{\circ }$.

The value of $\angle BAM=180-(28+90)=62^{\circ }$ .

So the value of $\angle BAD=55+62=117^{\circ }$ .

The value of $\angle ABD= 28^{\circ } , \angle ADC= 70^{\circ }$ and $\angle BAD= 117^{\circ }$ .

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