MATH SOLVE

4 months ago

Q:
# just answer this already......

Accepted Solution

A:

Answer:[tex]m\angle B=65\°[/tex][tex]m\angle C=140\°[/tex]Step-by-step explanation:From the figure ABCD given:[tex]BC=CD[/tex][tex]AB=AD[/tex][tex]m\angle A=90\°[/tex][tex]m\angle D=65\°[/tex]The given figure ABCD is a kite as it fulfills the properties of a kite.The properties of kite are:1) It is 4 sided2) 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:[tex]m\angle B=m\angle D[/tex]Given [tex]m\angle D=65\°[/tex]∴ [tex]m\angle B=65\°[/tex]Sum of interior angle of a quadrilateral = 360°So, we have [tex]m\angle A+m\angle B+m\angle C+m\angle D=360\°[/tex]Plugging in values of the angles known.[tex]90\°+65\°+m\angle C+65\°=360\°[/tex][tex]m\angle C+220\°=360\°[/tex]Using subtraction property of equality, we have[tex]m\angle C=360\°-220\°[/tex]∴ [tex]m\angle C=140\°[/tex]