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.