Question

The diagram shows a triangle ACD and an equilateral triangle BCD.

Answer 1

Answer:

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°