Question

1. ∠1 and ∠2 are complementary. m∠2 is six more than three times the m∠1. find the measure of both angles.

Explanation:

Step1: Recall complementary - angle relationship

Let \(m\angle1=x\) and \(m\angle2 = y\). Since \(\angle1\) and \(\angle2\) are complementary, \(x + y=90^{\circ}\). Also, given that \(y = 6x+3\).

Step2: Substitute \(y\) into the first - equation

Substitute \(y = 6x + 3\) into \(x + y=90^{\circ}\), we get \(x+(6x + 3)=90\).

Step3: Simplify the equation

Combine like terms: \(x+6x+3 = 90\), which simplifies to \(7x+3 = 90\).

Step4: Solve for \(x\)

Subtract 3 from both sides: \(7x=90 - 3=87\). Then \(x=\frac{87}{7}\approx12.43^{\circ}\).

Step5: Solve for \(y\)

Substitute \(x=\frac{87}{7}\) into \(y = 90 - x\), \(y=90-\frac{87}{7}=\frac{630 - 87}{7}=\frac{543}{7}\approx77.57^{\circ}\).

Answer:

\(m\angle1=\frac{87}{7}\approx12.43^{\circ}\), \(m\angle2=\frac{543}{7}\approx77.57^{\circ}\)