Given that ∠BCD and ∠BCA form a straight angle, if ∠BAC measures 20 degrees and ∠ABC measures 45 degrees, then the measure of ∠BCD is_____ degrees?

Question

Given that ∠BCD and ∠BCA form a straight angle,  if ∠BAC measures 20 degrees and ∠ABC measures 45 degrees, then the measure of ∠BCD is_____ degrees?

anonymous · Answer

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After drawing the diagram, you notice there is a triangle ABC. You know two of the measures (20 and 45) so to find the third angles measure (angle C) you would add 20 and 45 to get 65. Then subtract that amount from 180 since there are 180 total degrees in a triangle.180-65=115.

Angle ACB and angle BCD are supplementary. Now that you know angle ACB is 115, you can subtract that from 180 since that is what supplementary angles add up to. 180-115=65.