Question

Suppose a kite has two congruent angles of 100°. Of the remaining angles, one is four times larger than the other. What is the measure of the largest angle in the kite?

Answer 1

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

$A+B+C+D=360^o$

we have that

$A=B=100^o$

substitute

$100^o+100^o+C+D=360^o$

$C+D=160^o$ ----> equation A

Remember that

one is four times larger than the other

so

$C=4D$ ----> equation B

substitute equation B in equation A

$4D+D=160$

solve for D

$5D=160\\D=32^o$

Find the measure of angle C

$C=4(32)=128^o$

therefore

The measure of the largest angle in the kite is 128 degrees