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

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asked Oct 14, 2023 105k views

1 Answer

Dredful · Answer 1 · 2023-10-19T08:41:24+0000

Answer:

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.

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

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

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

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

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