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
if you give me a decimal i will sue this company
We can solve this problem using the fact that angles on a straight line sum up to 180 degrees.
Given that ∠ABD = 112°, we can write:
∠ABD + ∠CBD + ∠ABC = 180°
Substituting the given angle measures:
112° + (2x + 5) + (3x + 7) = 180°
Combine like terms:
5x + 124 = 180
Subtract 124 from both sides:
5x = 56
Divide both sides by 5:
x = 11.2
Now, substitute the value of x back into the equations to find the measures of ∠ABC and ∠CBD:
∠ABC = 3x + 7 = 3(11.2) + 7 = 33.6 + 7 = 40.6
∠CBD = 2x + 5 = 2(11.2) + 5 = 22.4 + 5 = 27.4
Therefore, ∠ABC measures approximately 40.6 degrees and ∠CBD measures approximately 27.4 degrees.