If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD? (2 points) ∠ABC= ° and ∠CBD= °
Since ∠ABD is 112°, we can solve for the measures of ∠ABC and ∠CBD using the fact that the sum of the angles in a triangle is 180°.
∠ABC + ∠ABD + ∠CBD = 180°
Substituting the value of ∠ABD, we have:
∠ABC + 112° + ∠CBD = 180°
To find the measures of ∠ABC and ∠CBD, we need more information about the triangle or the relationship between these angles.
my answer choices are
for ∠ABC 20,45,67,82
for ∠CBD 40,45,82,92
To find the measures of ∠ABC and ∠CBD with the given answer choices, we need to use the fact that the angles in a triangle add up to 180°.
Let's start by assigning values to ∠ABC and ∠CBD based on the answer choices:
- If ∠ABC = 20°, then ∠CBD = 180° - ∠ABD - ∠ABC = 180° - 112° - 20° = 48°.
- If ∠ABC = 45°, then ∠CBD = 180° - ∠ABD - ∠ABC = 180° - 112° - 45° = 23°.
- If ∠ABC = 67°, then ∠CBD = 180° - ∠ ABD - ∠ABC = 180° - 112° - 67° = 1°.
- If ∠ABC = 82°, then ∠CBD = 180° - ∠ABD - ∠ABC = 180° - 112° - 82° = -14°.
Since it is not possible for angles in a triangle to have negative measures, we can conclude that the only valid values for ∠ABC and ∠CBD are:
- ∠ABC = 45° and ∠CBD = 23°.
Therefore, ∠ABC= 45° and ∠CBD = 23° are the correct measures.
THERE IS NO 20 ONLY 25
Apologies for the previous mistake. If ∠ABC = 25°, then we can find ∠CBD using the fact that the angles in a triangle add up to 180°.
∠ABC + ∠ABD + ∠CBD = 180°
25° + 112° + ∠CBD = 180°
Simplifying the equation:
137° + ∠CBD = 180°
∠CBD = 180° - 137°
∠CBD = 43°
Therefore, ∠ABC = 25° and ∠CBD = 43°.
THERE IS NO 25 THERE IS ONLY 20
Apologies for the confusion. If ∠ABC = 20°, then we can find ∠CBD using the fact that the angles in a triangle add up to 180°.
∠ABC + ∠ABD + ∠CBD = 180°
20° + 112° + ∠CBD = 180°
Simplifying the equation:
132° + ∠CBD = 180°
∠CBD = 180° - 132°
∠CBD = 48°
Therefore, ∠ABC = 20° and ∠CBD = 48°.
THERE IS NO 48 ONLY 40 AND 45
Apologies for the confusion. Let's solve it correctly this time.
If ∠ABD is 112° and ∠ABC is 20°, then we can find ∠CBD using the fact that the angles in a triangle add up to 180°.
∠ABC + ∠ABD + ∠CBD = 180°
20° + 112° + ∠CBD = 180°
Simplifying the equation:
132° + ∠CBD = 180°
∠CBD = 180° - 132°
∠CBD = 48°
Therefore, ∠ABC = 20° and ∠CBD = 48°.