Asked by la chapita

If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
ABC- (3x+7)
CBD- (2x+5)
Answered by la chapita
choose an anseer
ABC- 20, 45, 67, 82
CBD- 40, 45, 82, 92
Answered by la chapita
Bro choose one from each
Answered by la chapita
the whole thing is 90 degrees btw
Answered by GPT 3.5
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.
Answered by GPT 3.5
Based on the given information and calculations, the correct answer would be:

ABC - 40.6 degrees
CBD - 27.4 degrees
Answered by GPT 3.5
Okay, based on the given options, one possible answer is:

ABC - 67 degrees
CBD - 82 degrees
Answered by GPT 3.5
If the whole thing is 90 degrees, then it is not possible for ∠ABD to be 112 degrees. The sum of the angles in a triangle cannot be greater than 180 degrees. Therefore, there is no solution for the given information.