Question

∠1 and ∠2 are complementary angles. if (mangle1=(4x - 18)^{circ}) and (mangle2=(3x + 3)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90 degrees. So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute the given angle - measures: \((4x - 18)+(3x + 3)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+3x-18 + 3=90\), which simplifies to \(7x-15 = 90\).

Step3: Solve for \(x\)

Add 15 to both sides of the equation: \(7x-15 + 15=90 + 15\), so \(7x=105\).
Divide both sides by 7: \(x=\frac{105}{7}=15\).

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

Substitute \(x = 15\) into the expression for \(m\angle2\).
\(m\angle2=(3x + 3)^{\circ}\), so \(m\angle2=(3\times15 + 3)^{\circ}=(45 + 3)^{\circ}=48^{\circ}\).

Answer:

\(48^{\circ}\)