Answer:
x = 72°
y = 123°
Step-by-step explanation:
Angles around a point sum to 360°.
As the diagram is made from 5 congruent kites, find the value of x by dividing 360° by 5:
[tex]\implies x=\dfrac{360^{\circ}}5}=72^{\circ}[/tex]
A kite is a quadrilateral, so the sum of its interior angles is 360°.
The opposite obtuse angles of a kite are congruent.
[tex]\implies x+2y+42^{\circ}=360^{\circ}[/tex]
[tex]\implies 72^{\circ}+2y+42^{\circ}=360^{\circ}[/tex]
[tex]\implies 2y+114^{\circ}=360^{\circ}[/tex]
[tex]\implies 2y=246^{\circ}[/tex]
[tex]\implies y=123^{\circ}[/tex]
