Question

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Answer 1

Answer:

$m\angle B=65\°$

$m\angle C=140\°$

Step-by-step 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

$m\angle C=360\°-220\°$

∴ $m\angle C=140\°$