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Question

asked Sep 4, 2020 102k views

1 Answer

Mikhail Melnik · Answer 1 · 2020-09-10T20:43:56+0000

Answer:

$m\angle B=65\°$

$m\angle C=140\°$

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

$m\angle C=360\°-220\°$

∴
$m\angle C=140\°$