To find the measures of ∠ABC and ∠CBD, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
Since ∠ABD is 112°, we know that ∠ABC + ∠CBD + ∠ABD = 180°.
Let's substitute the given expressions for the angles into this equation:
(3x + 7) + (2x + 5) + 112 = 180
Simplifying the equation:
5x + 124 = 180
Next, let's solve for x:
5x = 180 - 124
5x = 56
x = 56 / 5
x = 11.2
Now, we can find the measures of ∠ABC and ∠CBD by substituting the value of x into their respective expressions:
∠ABC = 3x + 7 = 3(11.2) + 7 = 33.6 + 7 = 40.6 degrees
∠CBD = 2x + 5 = 2(11.2) + 5 = 22.4 + 5 = 27.4 degrees
Therefore, the measures of ∠ABC and ∠CBD are 40.6 degrees and 27.4 degrees, respectively.
If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
angle abc: (3x+7) degrees
angle cbd: (2x+5) degrees
1 answer