Answer:
Part 1) [tex]x=35^o[/tex]
Part 2) [tex]y=30^o[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
The diagonal of the figure divide the kite into two congruent triangles
so
[tex](3x+5)^o=(4x-30)^o[/tex]
solve for x
Group terms
[tex]4x-3x=5+30[/tex]
[tex]x=35^o[/tex]
Part 2) Find the value of y
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]y^o+(3x+5)^o+(2y-20)^o=180^o[/tex]
substitute the value of x
[tex]y^o+(3(35)+5)^o+(2y-20)^o=180^o[/tex]
[tex]y^o+(110)^o+(2y-20)^o=180^o[/tex]
solve for y
combine like terms
[tex](3y+90)^o=180^o[/tex]
[tex]3y=90^o[/tex]
[tex]y=30^o[/tex]
