Question

1. if ( mangle b ) is two more than three times the measure of ( angle c ), and ( angle b ) and ( angle c ) are complementary angles, find each angle measure.

Explanation:

Step1: Set up equations

Let \(m\angle C = x\). Then \(m\angle B=3x + 2\). Since \(\angle B\) and \(\angle C\) are complementary, \(m\angle B+m\angle C = 90^{\circ}\). So the equation is \((3x + 2)+x=90\).

Step2: Solve the equation

Combine like - terms: \(4x+2 = 90\).
Subtract 2 from both sides: \(4x=90 - 2=88\).
Divide both sides by 4: \(x=\frac{88}{4}=22\).

Step3: Find \(m\angle B\)

Substitute \(x = 22\) into \(m\angle B=3x + 2\). Then \(m\angle B=3\times22+2=66 + 2=68\).

Answer:

\(m\angle C = 22^{\circ}\) and \(m\angle B=68^{\circ}\)