Question

1. ∠1 and ∠2 form a linear pair. if m∠1=(5x + 7)° and m∠2=(3x + 5)°, find the measure of each angle.

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, so \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1=(5x + 7)^{\circ}\) and \(m\angle2=(3x + 5)^{\circ}\), we have the equation \((5x + 7)+(3x + 5)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+3x+7 + 5=180\), which simplifies to \(8x+12 = 180\).

Step3: Isolate the variable term

Subtract 12 from both sides of the equation: \(8x=180 - 12\), so \(8x=168\).

Step4: Solve for \(x\)

Divide both sides by 8: \(x=\frac{168}{8}=21\).

Step5: Find \(m\angle1\)

Substitute \(x = 21\) into the expression for \(m\angle1\): \(m\angle1=5x+7=5\times21 + 7=105 + 7=112^{\circ}\).

Step6: Find \(m\angle2\)

Substitute \(x = 21\) into the expression for \(m\angle2\): \(m\angle2=3x+5=3\times21+5=63 + 5=68^{\circ}\).

Answer:

\(m\angle1 = 112^{\circ}\), \(m\angle2=68^{\circ}\)