Question

1. complete a two - column proof:

given: < cea and < ceb are supplementary
prove: x = 40

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(y + 20=4y-15\).
Subtract \(y\) from both sides: \(20 = 3y-15\).
Add 15 to both sides: \(35=3y\).
Divide by 3: \(y=\frac{35}{3}\) (This step is wrong. Wait, actually, \(\angle CEA=(y + 20)+(4y-15)\) and \(\angle CEB=(3x + 5)+(x + 15)\). Since \(\angle CEA\) and \(\angle CEB\) are supplementary, \(\angle CEA+\angle CEB = 180^{\circ}\). Also, \((y + 20)\) and \((x + 15)\) are vertical angles (\(y+20=x + 15\)), and \((4y-15)\) and \((3x + 5)\) are vertical angles (\(4y-15=3x + 5\)).

From \(y+20=x + 15\), we get \(y=x - 5\).

Substitute \(y=x - 5\) into \(4y-15=3x + 5\).

Step2: Substitute and solve

Substitute \(y=x - 5\) into \(4y-15=3x + 5\):

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Answer:

\(x = 40\)