Questions: x= m∠ABD= m∠CBD= -4x+33 ≠ 2x+81 -3-3 -4x=2x+48 -3x -6x/-6 = -48/-6 = 42 x=8

x= m∠ABD= m∠CBD= -4x+33 ≠ 2x+81 -3-3 -4x=2x+48 -3x -6x/-6 = -48/-6 = 42 x=8
Transcript text: $x=$ $\qquad$ $\mathrm{m} \angle A B D=$ $\qquad$ $\mathrm{m} \angle C B D=$ $\qquad$ \[ \begin{array}{c} -4 x+33 \neq 2 x+81 \\ -3-3 \\ -4 x=2 x+48 \\ -3 x \\ \frac{-6 x}{-6}=\frac{-48}{-6}=42 \\ x=8 \end{array} \]
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Solution

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Solution Steps

Step 1: Set up the equation

The angles ∠ABD and ∠CBD are adjacent and form a straight angle, so their sum is 180°. Therefore, (-4x + 33) + (2x + 81) = 180

Step 2: Solve for x

Combine like terms: -2x + 114 = 180 Subtract 114 from both sides: -2x = 66 Divide both sides by -2: x = -33

Step 3: Calculate m∠ABD

Substitute x = -33 into the expression for m∠ABD: m∠ABD = -4(-33) + 33 = 132 + 33 = 165°

Step 4: Calculate m∠CBD

Substitute x = -33 into the expression for m∠CBD: m∠CBD = 2(-33) + 81 = -66 + 81 = 15°

Final Answer

x = -33, m∠ABD = 165°, m∠CBD = 15°

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