If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
(2 points)
∠ABC=
° and ∠CBD=
°
Since ∠ABD is 112°, and ∠ABC and ∠CBD are adjacent angles, they form a straight line with ∠ABD. Therefore, the sum of ∠ABC and ∠CBD must be 180°.
∠ABC + ∠CBD = 180°
Let's solve for ∠ABC:
∠ABC + ∠CBD = 180°
∠ABC + 112° = 180°
Subtracting 112° from both sides:
∠ABC = 180° - 112°
∠ABC = 68°
Now, let's solve for ∠CBD:
∠ABC + ∠CBD = 180°
68° + ∠CBD = 180°
Subtracting 68° from both sides:
∠CBD = 180° - 68°
∠CBD = 112°
Therefore, ∠ABC = 68° and ∠CBD = 112°.
ABC = (3x + 7)
CBD = (2x + 5)
Since ∠ABC and ∠CBD are adjacent angles, they form a straight line with ∠ABD. Therefore, the sum of ∠ABC and ∠CBD must be 180°.
∠ABC + ∠CBD = 180°
But we are given that ∠ABC = 3x + 7 and ∠CBD = 2x + 5. So we can substitute these values into the equation:
(3x + 7) + (2x + 5) = 180°
Combining like terms, we get:
3x + 2x + 7 + 5 = 180°
5x + 12 = 180°
Now, we can solve for x. Subtracting 12 from both sides:
5x = 180° - 12
5x = 168°
Now, divide both sides by 5 to solve for x:
x = 168° / 5
x = 33.6°
Now that we have the value of x, we can substitute it back into the expressions for ∠ABC and ∠CBD to find their values.
∠ABC = 3x + 7
∠ABC = 3(33.6°) + 7
∠ABC = 100.8° + 7
∠ABC = 107.8°
∠CBD = 2x + 5
∠CBD = 2(33.6°) + 5
∠CBD = 67.2° + 5
∠CBD = 72.2°
Therefore, ∠ABC = 107.8° and ∠CBD = 72.2°.