Question

13 The diagram is made from 5 congruent kites, Work out the value of (a) %, (b) y. NOT TO SCALE ya (2​

Answer 1

x = 72°

y = 123°

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:

`\implies x=\frac{360^(\circ)}5}=72^(\circ)`

A kite is a quadrilateral, so the sum of its interior angles is 360°.

The opposite obtuse angles of a kite are congruent.

`\implies x+2y+42^(\circ)=360^(\circ)`

`\implies 72^(\circ)+2y+42^(\circ)=360^(\circ)`

`\implies 2y+114^(\circ)=360^(\circ)`

`\implies 2y=246^(\circ)`

`\implies y=123^(\circ)`