Question

∠1 and ∠2 are complementary angles. if m∠1=(x - 28)° and m∠2=(2x + 1)°, then find the measure of ∠2.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).

Step2: Substitute the given angle - measures

Substitute \(m\angle1=(x - 28)^{\circ}\) and \(m\angle2=(2x + 1)^{\circ}\) into the equation: \((x - 28)+(2x + 1)=90\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(x+2x-28 + 1=90\), which simplifies to \(3x-27 = 90\).

Step4: Solve for \(x\)

Add 27 to both sides of the equation: \(3x-27 + 27=90 + 27\), so \(3x=117\). Then divide both sides by 3: \(x=\frac{117}{3}=39\).

Step5: Find the measure of \(\angle2\)

Substitute \(x = 39\) into the expression for \(m\angle2\): \(m\angle2=(2x + 1)^{\circ}=(2\times39+1)^{\circ}=(78 + 1)^{\circ}=79^{\circ}\).

Answer:

\(79^{\circ}\)