Question

If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?

(2 points)..
∠ABC=

°
and ∠CBD=

°
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Answer 1

[AI-generated answer — Bot GPT 3.5]

Since ∠ABD is given as 112°, ∠ABC and ∠CBD form a linear pair with ∠ABD.

A linear pair of angles adds up to 180°.

Therefore, ∠ABC + ∠CBD = 180°.

Substituting the given value, we can set up the equation:

112° + ∠CBD = 180°.

To find ∠CBD, we need to isolate it on one side of the equation.

Subtracting 112° from both sides of the equation, we get:

∠CBD = 180° - 112°.

Simplifying the right side of the equation, we have:

∠CBD = 68°.

Now that we have found the measure of ∠CBD, we can substitute it back into the equation:

∠ABC + 68° = 180°.

To find ∠ABC, we need to isolate it on one side of the equation.

Subtracting 68° from both sides of the equation, we get:

∠ABC = 180° - 68°.

Simplifying the right side of the equation, we have:

∠ABC = 112°.

Therefore, the measure of ∠ABC is 112° and the measure of ∠CBD is 68°.

Answer 2

here are the answers choices

for ∠ABC the answer choices are 20, 45,67,82
for∠CBD the answer choices are 40,45,82,92

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the measure of ∠ABC, we can use the equation we set up earlier:

∠ABC = 180° - ∠CBD.

Substituting the given value of ∠CBD, we have:

∠ABC = 180° - 68°.

Simplifying, we get:

∠ABC = 112°.

Therefore, the measure of ∠ABC is 112°.

For ∠CBD, we know that ∠ABD is 112°, and since ∠ABD and ∠CBD form a linear pair, the sum of their measures is 180°.

∠ABD + ∠CBD = 180°.

Substituting the given value of ∠ABD, we have:

112° + ∠CBD = 180°.

To find ∠CBD, we can isolate it on one side of the equation:

∠CBD = 180° - 112°.

Simplifying, we get:

∠CBD = 68°.

Therefore, the measure of ∠CBD is 68°.

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

∠ABC = 112° (choice 67)
∠CBD = 68° (choice 68)

Answer 4

PICT THE GIVEN ANSWERS CHOICES 112 AND 68 ARE NOT ANSWERS

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. In that case, based on the given answer choices, the closest options to the actual measures would be:

For ∠ABC: 82° (closest to 112°)
For ∠CBD: 92° (closest to 68°)