Answer:
The measure of the largest angle in the kite is 128 degrees
Step-by-step explanation:
we know that
The sum of the interior angles in any quadrilateral must be equal to 360 degrees
A kite is a quadrilateral
Let
A,B,C and D the measure of the interior angles
so
[tex]A+B+C+D=360^o[/tex]
we have that
[tex]A=B=100^o[/tex]
substitute
[tex]100^o+100^o+C+D=360^o[/tex]
[tex]C+D=160^o[/tex] ----> equation A
Remember that
one is four times larger than the other
so
[tex]C=4D[/tex] ----> equation B
substitute equation B in equation A
[tex]4D+D=160[/tex]
solve for D
[tex]5D=160\\D=32^o[/tex]
Find the measure of angle C
[tex]C=4(32)=128^o[/tex]
therefore
The measure of the largest angle in the kite is 128 degrees
