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∠1 and ∠2 are complementary angles. if m∠1 = (8x - 12)° and m∠2 = (6x + 18)°, then find the measure of ∠1.
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Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(8x - 12)^{\circ}\) and \(m\angle2=(6x + 18)^{\circ}\) into the equation:
\((8x - 12)+(6x + 18)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(8x+6x-12 + 18=90\), which simplifies to \(14x+6 = 90\).

Step3: Solve for \(x\)

Subtract \(6\) from both sides: \(14x=90 - 6=84\).
Divide both sides by \(14\): \(x=\frac{84}{14}=6\).

Step4: Find the measure of \(\angle1\)

Substitute \(x = 6\) into \(m\angle1=(8x - 12)^{\circ}\).
\(m\angle1=(8\times6-12)^{\circ}=(48 - 12)^{\circ}=36^{\circ}\).

Answer:

\(36\)