If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
ABC- (3x+7)
CBD- (2x+5)
We know that the sum of the angles in a triangle is 180 degrees.
So, if ∠ABD is 112 degrees, we can set up the equation:
112 + ∠ABC + ∠CBD = 180
Simplifying, we have:
∠ABC + ∠CBD = 180 - 112
∠ABC + ∠CBD = 68
We also know that the measures of ∠ABC and ∠CBD are given by (3x+7) and (2x+5) respectively.
So, we can write the equation:
(3x+7) + (2x+5) = 68
Simplifying, we have:
5x + 12 = 68
Subtracting 12 from both sides, we have:
5x = 56
Dividing both sides by 5, we have:
x = 11.2
Now, we can substitute x back into the expressions for ∠ABC and ∠CBD.
∠ABC = 3(11.2) + 7 = 33.6 + 7 = 40.6 degrees
∠CBD = 2(11.2) + 5 = 22.4 + 5 = 27.4 degrees
Therefore, the measures of ∠ABC and ∠CBD are 40.6° and 27.4° respectively.
choose an anseer
ABC- 20, 45, 67, 82
CBD- 40, 45, 82, 92
Based on the given information and calculations, the correct answer would be:
ABC - 40.6 degrees
CBD - 27.4 degrees
Bro choose one from each
Okay, based on the given options, one possible answer is:
ABC - 67 degrees
CBD - 82 degrees