Question

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Explanation:

1. Explanation:

• Since \(\angle POQ\) is a straight - angle, its measure is \(180^{\circ}\). The sum of the angles \(\angle POS\), \(\angle SOR\), and \(\angle ROQ\) is equal to \(\angle POQ\).
• Step 1: Set up the equation
• We know that \((5x + 4)+(x - 2)+(3x + 7)=180\).
• First, combine like - terms on the left - hand side of the equation. Combine the \(x\) terms: \(5x+x + 3x=9x\), and combine the constant terms: \(4-2 + 7=9\). So the equation becomes \(9x+9 = 180\).
• Step 2: Solve for \(x\)
• Subtract 9 from both sides of the equation: \(9x+9-9=180 - 9\), which simplifies to \(9x=171\).
• Then divide both sides by 9: \(x=\frac{171}{9}=19\).

1. Answer:

• \(x = 19\)

Answer:

1. Explanation:

• Since \(\angle POQ\) is a straight - angle, its measure is \(180^{\circ}\). The sum of the angles \(\angle POS\), \(\angle SOR\), and \(\angle ROQ\) is equal to \(\angle POQ\).
• Step 1: Set up the equation
• We know that \((5x + 4)+(x - 2)+(3x + 7)=180\).
• First, combine like - terms on the left - hand side of the equation. Combine the \(x\) terms: \(5x+x + 3x=9x\), and combine the constant terms: \(4-2 + 7=9\). So the equation becomes \(9x+9 = 180\).
• Step 2: Solve for \(x\)
• Subtract 9 from both sides of the equation: \(9x+9-9=180 - 9\), which simplifies to \(9x=171\).
• Then divide both sides by 9: \(x=\frac{171}{9}=19\).

1. Answer:

• \(x = 19\)