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Consider the hexagon ABCDEF.What is the measure of angle BCG?

Consider the hexagon ABCDEF.What is the measure of angle BCG?-example-1
User Joe Ferris
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1 Answer

7 votes

The sum of the interior angles of a hexagon is 720°. Then:

2x + 6 + 2x + 2x + 16 + 145 + 130 + 3x = 720

Combining similar terms

(2x + 2x + 2x + 3x) + (6 + 16 + 145 + 130) = 720

9x + 297 = 720

297 is adding on the left, then it will subtract on the right

9x = 720 - 297

9x = 423

9 is multiplying on the left, then it will divide on the right

x = 423/9

x = 47

Now, we can compute angle BCD, as follows:

∠BCD = 2x + 16

∠BCD = 2(47) + 16

∠BCD = 110°

∠BCD and ∠BCG are supplementary, then:

∠BCD + ∠BCG = 180°

110° + ∠BCG = 180°

∠BCG = 180° - 110°

∠BCG = 70°

User BlackSlash
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