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∠1 and ∠2 are vertical angles. if ( m∠1=(7x + 14)^{circ} ) and ( m∠2=(3x + 30)^{circ} ), then find the measure of
∠1.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, \(7x + 14=3x + 30\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(7x-3x + 14=3x-3x + 30\), which simplifies to \(4x+14 = 30\).
Subtract \(14\) from both sides: \(4x+14 - 14=30 - 14\), so \(4x=16\).
Divide both sides by \(4\): \(x=\frac{16}{4}=4\).

Step3: Find the measure of \(\angle1\)

Substitute \(x = 4\) into \(m\angle1=(7x + 14)^{\circ}\).
\(m\angle1=(7\times4 + 14)^{\circ}=(28+14)^{\circ}=42^{\circ}\).

Answer:

\(42^{\circ}\)