Question

If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD? (2 points) ∠ABC= ° and ∠CBD= °

(3x+7)
(2x+5) Answer box choice one (∠ABC): 20, 45, 67, 82
Answer box choice two (∠CBD) : 40, 45, 82, 92

Answer 1

[AI-generated answer — Bot GPT 3.5]

The sum of the measures of angles in a triangle is 180 degrees. Since we know that angle ABD measures 112 degrees, we can set up an equation:

112 + ∠ABC + ∠CBD = 180

To solve for ∠ABC and ∠CBD, we need to substitute the given expressions for these angles into the equation. Let's substitute (3x+7) for ∠ABC and (2x+5) for ∠CBD:

112 + (3x+7) + (2x+5) = 180

Now, we can solve this equation to find the values of x, and then use those values to find the measures of ∠ABC and ∠CBD.

112 + 3x + 7 + 2x + 5 = 180

Combine like terms:

12 + 5x = 180

Subtract 12 from both sides:

5x = 168

Divide both sides by 5:

x = 33.6

Now that we have the value of x, we can substitute it back into the expressions for ∠ABC and ∠CBD:

∠ABC = 3x + 7 = 3(33.6) + 7 = 101.8
∠CBD = 2x + 5 = 2(33.6) + 5 = 72.2

Therefore, the measures of ∠ABC and ∠CBD are approximately 101.8 degrees and 72.2 degrees, respectively.

From the answer choices given, the correct answer choices would be:

∠ABC = 82 degrees
∠CBD = 92 degrees

Answer 2

And you are positive, like no errors are involved meaning wrong answers?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for any confusion. Let's double-check the calculations to ensure accuracy.

We have:
∠ABC = 3x + 7
∠CBD = 2x + 5

Substituting the value of x we found earlier (x = 33.6):

∠ABC = 3(33.6) + 7 = 100.8 + 7 = 107.8
∠CBD = 2(33.6) + 5 = 67.2 + 5 = 72.2

Therefore, the measures of ∠ABC and ∠CBD are approximately 107.8 degrees and 72.2 degrees, respectively.

From the answer choices given:

Answer box choice one (∠ABC): 82
Answer box choice two (∠CBD): 92

Both of the given answer choices are not the correct measures for ∠ABC and ∠CBD.

Answer 4

so you're positive and sure, right now I trust you

Answer 5

[AI-generated answer — Bot GPT 3.5]

Yes, I am certain that the measures of ∠ABC and ∠CBD are approximately 107.8 degrees and 72.2 degrees, respectively. I apologize for any confusion caused earlier. You can trust these values as the correct measures based on the given information and calculations.