The diagram shows a triangle ACD and an equilateral triangle BCD. Work out the size of angle x.
(2 points)
с
Not drawn
accurately
409
А
B.
D

x = 20°

Step-by-step explanation:

An equilateral triangle has three equal angles of 60° each.

Since ∆BCD is an equilateral triangle, it follows that:

<CBD = <BCD = <CDB = 60°

m<ACD = 40° + <BCD

m<ACD = 40° + 60° (substitution)

m<ACD = 100°

x + m<ACD + CDB = 180° (sum of triangle)

x + 100° + 60° = 180° (substitution)

x + 160 = 180

Subtract 160 from each side

x = 180 - 160

x = 20°

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