Question

∠1 and ∠2 are complementary angles. if m∠1 = (4x + 12)° and m∠2 = (3x - 6)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(4x + 12)^{\circ}\) and \(m\angle2=(3x - 6)^{\circ}\) into the equation:
\((4x + 12)+(3x - 6)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(4x+3x+12 - 6=90\)
\(7x + 6=90\)

Step3: Solve for \(x\)

Subtract \(6\) from both sides:
\(7x=90 - 6\)
\(7x=84\)
Divide both sides by \(7\):
\(x=\frac{84}{7}=12\)

Step4: Find the measure of \(\angle2\)

Substitute \(x = 12\) into \(m\angle2=(3x - 6)^{\circ}\)
\(m\angle2=(3\times12-6)^{\circ}\)
\(m\angle2=(36 - 6)^{\circ}\)
\(m\angle2 = 30^{\circ}\)

Answer:

\(30^{\circ}\)