Question

If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?(2 points)∠ABC=°and ∠CBD=°
Number options for ABC
A. 20
B. 45
C. 67
D. 82
Number options for CBD
A. 40
B. 45
C. 82
D. 92
Answer
JUST CHOOSE
Answer
THAT'S 174
Answered by GPT 3.5
The measures of ∠ABC and ∠CBD can be found using the Angle Addition Postulate, which states that the measure of the whole angle (∠ABD) is equal to the sum of the measures of its two parts (∠ABC and ∠CBD).

Thus, ∠ABD = ∠ABC + ∠CBD.

Given that ∠ABD = 112°, we can substitute this value into the equation:

112° = ∠ABC + ∠CBD.

To find the values of ∠ABC and ∠CBD, we can try out the given number options until we obtain a sum of 112°.

Let's test out the options:
1. Option A: ∠ABC = 20°, ∠CBD = 40°
∠ABC + ∠CBD = 20° + 40° = 60° ≠ 112°

2. Option B: ∠ABC = 45°, ∠CBD = 45°
∠ABC + ∠CBD = 45° + 45° = 90° ≠ 112°

3. Option C: ∠ABC = 67°, ∠CBD = 82°
∠ABC + ∠CBD = 67° + 82° = 149° ≠ 112°

4. Option D: ∠ABC = 82°, ∠CBD = 92°
∠ABC + ∠CBD = 82° + 92° = 174° ≠ 112°

None of the options listed above give a sum of 112°. Therefore, the measures of ∠ABC and ∠CBD are not among the given number options.
Answered by GPT 3.5
Based on the given number options, the closest sum to 112° is option D. Therefore:

∠ABC = 82°
∠CBD = 92°
Answered by GPT 3.5
Apologies for the error. Let's try one more time:

Based on the given number options, the closest sum to 112° is option C. Therefore:

∠ABC = 67°
∠CBD = 82°