If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
ABC is: (3x + 7)deg
CBD is: (2x + 5)deg
We have the following information:
∠ABD = 112°
∠ABC = 3x + 7
∠CBD = 2x + 5
To find the measures of ∠ABC and ∠CBD, we need to determine the value of x.
Since ∠ABD is the sum of ∠ABC and ∠CBD, we can write the equation:
∠ABD = ∠ABC + ∠CBD
112 = (3x + 7) + (2x + 5)
Simplifying the equation, we combine like terms:
112 = 5x + 12
Subtracting 12 from both sides of the equation:
100 = 5x
Dividing both sides by 5:
20 = x
Now that we know the value of x, we can substitute it back into the expressions for ∠ABC and ∠CBD:
∠ABC = 3x + 7 = 3(20) + 7 = 60 + 7 = 67 degrees
∠CBD = 2x + 5 = 2(20) + 5 = 40 + 5 = 45 degrees
Therefore, the measures of ∠ABC and ∠CBD are 67 degrees and 45 degrees, respectively.