If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
Responses for ABC:
20
45
67
82
Responses for CBD:
40
45
82
92
Given that ∠ABD measures 112°, we can find ∠ABC and ∠CBD by using the property that the sum of the angles in a triangle is always 180°.
∠ABD = ∠ABC + ∠CBD
Substituting in the values we have:
112 = ∠ABC + ∠CBD
To find the possible measures of ∠ABC and ∠CBD, we can use trial and error.
Trying the given options for ∠ABC:
1. If ∠ABC = 20, then ∠CBD = 112 - 20 = 92 (Not a match)
2. If ∠ABC = 45, then ∠CBD = 112 - 45 = 67 (Not a match)
3. If ∠ABC = 67, then ∠CBD = 112 - 67 = 45 (Match!)
4. If ∠ABC = 82, then ∠CBD = 112 - 82 = 30 (Not a match)
From the options provided, the possible measure for ∠ABC is 67.
From the options provided, the possible measure for ∠CBD is 45.