Question

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Answer 1

`m\angle B=65\°`

`m\angle C=140\°`

Explanation:

From the figure ABCD given:

`BC=CD`

`AB=AD`

`m\angle A=90\°`

`m\angle D=65\°`

The given figure ABCD is a kite as it fulfills the properties of a kite.

The properties of kite are:

1) It is 4 sided

2) It has 2 pairs of equal sides adjacent to each other.

3) The angles formed between the 2 pairs of sides is equal.

By the 3rd property of kite stated above:

`m\angle B=m\angle D`

Given
`m\angle D=65\°`

∴
`m\angle B=65\°`

Sum of interior angle of a quadrilateral = 360°

So, we have
`m\angle A+m\angle B+m\angle C+m\angle D=360\°`

Plugging in values of the angles known.

`90\°+65\°+m\angle C+65\°=360\°`

`m\angle C+220\°=360\°`

Using subtraction property of equality, we have

`m\angle C=360\°-220\°`

∴
`m\angle C=140\°`