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°.
If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
(2 points)..
∠ABC=
°
and ∠CBD=
°
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5 answers
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
for ∠ABC the answer choices are 20, 45,67,82
for∠CBD the answer choices are 40,45,82,92
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)
∠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)
PICT THE GIVEN ANSWERS CHOICES 112 AND 68 ARE NOT ANSWERS
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°)
For ∠ABC: 82° (closest to 112°)
For ∠CBD: 92° (closest to 68°)