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

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

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