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
no decimals full numbers
To find the measures of ∠ABC and ∠CBD, we will use the fact that the sum of the angles in a triangle is 180°.
Given that ∠ABD is 112°, we can set up the equation:
∠ABD + ∠ABC + ∠CBD = 180°
Substituting the given expressions for ∠ABC and ∠CBD:
112° + (3x + 7)° + (2x + 5)° = 180°
Combine like terms:
112° + 3x + 7° + 2x + 5° = 180°
5x + 124° = 180°
Subtract 124° from both sides:
5x = 56°
Divide both sides by 5:
x = 11.2°
To find ∠ABC and ∠CBD, substitute the value of x back into the expressions:
∠ABC = 3x + 7
∠ABC = 3(11.2) + 7
∠ABC = 33.6 + 7
∠ABC = 40.6°
∠CBD = 2x + 5
∠CBD = 2(11.2) + 5
∠CBD = 22.4 + 5
∠CBD = 27.4°
Therefore, the measures of ∠ABC and ∠CBD are approximately 40.6° and 27.4°, respectively.