If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD? (2 points) ∠ABC= ° and ∠CBD= °
(3x+7)
(2x+5)
To find the measures of ∠ABC and ∠CBD, we need to set up an equation using the fact that the sum of the angles in a triangle is 180 degrees.
We know that ∠ABD = 112°, so we can substitute it into the equation below:
∠ABC + ∠ABD + ∠CBD = 180°
Plugging in the expressions in parentheses for ∠ABC and ∠CBD, we get:
(3x + 7) + 112° + (2x + 5) = 180°
Simplifying the equation, we combine like terms:
5x + 124 = 180
Next, we isolate the variable by subtracting 124 from both sides:
5x = 56
Finally, we solve for x by dividing both sides by 5:
x = 56/5
Therefore, x = 11.2.
To find the measures of ∠ABC and ∠CBD, we substitute the value of x back into their expressions:
∠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, the measures of ∠ABC and ∠CBD are ∠ABC = 40.6° and ∠CBD = 27.4°.
The answer choices are:
20, 45, 67, 82
and
40, 45, 82, 92
To find the measures of ∠ABC and ∠CBD, we need to substitute the given values into the expressions for ∠ABC and ∠CBD.
From the expression (3x + 7), we substitute x with its corresponding value of 11.2:
∠ABC = 3(11.2) + 7 = 33.6 + 7 = 40.6°
From the expression (2x + 5), we substitute x with its corresponding value of 11.2:
∠CBD = 2(11.2) + 5 = 22.4 + 5 = 27.4°
Therefore, the correct choices are:
∠ABC = 40.6°
∠CBD = 27.4°
Among the answer choices:
20, 45, 67, 82
None of these choices match the measured values of ∠ABC = 40.6° and ∠CBD = 27.4°.
Among the answer choices:
40, 45, 82, 92
∠ABC = 40.6° matches the first value of 40 in the choices, and ∠CBD = 27.4° does not match any of the choices.
Hence, the only correct measure among the answer choices is:
∠ABC = 40°.