Question

Find x and y
Show all the work

Answer 1

Given:

A geometric figure.

To find:

The values of x and y.

Solution:

The given figure is a kite because it has two disjoint pairs of consecutive congruent sides.

Kite has one pair of congruent opposite angles. The angled included between non-congruent sides are congruent.

`(4x+13)^\circ=(5x-15)^\circ`

`4x+13=5x-15`

`13+15=5x-4x`

`28=x`

The diagonal bisects the other pair of opposite angles.

The missing angle of the above triangle is
`y^\circ`.

Using angle sum property, we get

`(y-9)^\circ+y^\circ+(4x+13)^\circ=180^\circ`

`(2y-9)^\circ+(4(28)+13)^\circ=180^\circ`

`(2y-9)^\circ+(125)^\circ=180^\circ`

`(2y-9)^\circ=180^\circ-125^\circ`

On further simplification, we get

`(2y-9)^\circ=55^\circ`

`2y-9=55`

`2y=55+9`

`2y=64`

Divide both sides by 2.

`y=32`

Therefore, the value of x is 28 and the value of y is 32.