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The angle BCD = 120°

Further explanation

Given

A parallelogram and four angles

Required

Angle BCD

Solution

In A parallelogram

The sum of the four angles is 360°

Opposite angles are equal /congruent(A=C, B=D)

Consecutive angles are supplementary (A + D = 180 °, D + C = 180°, C + B = 180°, B + A = 180°).

We choose a solution by using

Consecutive angles :

∠C+∠B=180°

18x=180°

x=10

∠C=∠BCD =

[tex]\tt 12x=12\times 10=120^o[/tex]

Or we can use another ways :

The sum of the four angles is 360°

∠A+∠B+∠C+∠D=360°

12x+6x+12x+6x=360°

36x=360°

x=10

∠C=∠BCD =

[tex]\tt 12x=12\times 10=120^o[/tex]

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