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.
[tex](4x+13)^\circ=(5x-15)^\circ[/tex]
[tex]4x+13=5x-15[/tex]
[tex]13+15=5x-4x[/tex]
[tex]28=x[/tex]
The diagonal bisects the other pair of opposite angles.
The missing angle of the above triangle is [tex]y^\circ[/tex].
Using angle sum property, we get
[tex](y-9)^\circ+y^\circ+(4x+13)^\circ=180^\circ[/tex]
[tex](2y-9)^\circ+(4(28)+13)^\circ=180^\circ[/tex]
[tex](2y-9)^\circ+(125)^\circ=180^\circ[/tex]
[tex](2y-9)^\circ=180^\circ-125^\circ[/tex]
On further simplification, we get
[tex](2y-9)^\circ=55^\circ[/tex]
[tex]2y-9=55[/tex]
[tex]2y=55+9[/tex]
[tex]2y=64[/tex]
Divide both sides by 2.
[tex]y=32[/tex]
Therefore, the value of x is 28 and the value of y is 32.