Question

∠1 and ∠2 are complementary angles. if ( m∠1=(3x - 28)^{circ} ) and ( m∠2=(x + 18)^{circ} ), then find the measure of ∠1.

Explanation:

Step1: Use complementary angles property

Complementary angles sum to \(90^{\circ}\). So, \((3x - 28)+(x + 18)=90\).

Step2: Simplify the equation

Combine like terms: \(3x+x-28 + 18=90\), which becomes \(4x-10 = 90\).

Step3: Solve for \(x\)

Add \(10\) to both sides: \(4x=90 + 10=100\). Then divide by \(4\): \(x=\frac{100}{4}=25\).

Step4: Find \(m\angle1\)

Substitute \(x = 25\) into \(m\angle1=(3x - 28)^{\circ}\). So, \(m\angle1=(3\times25-28)^{\circ}=(75 - 28)^{\circ}=47^{\circ}\).

Answer:

\(47\)