Question

1. given that ∠1 = 3x, ∠2 = x + 10 and ∠3 = 2x + 14, what is the measure of ∠2?

a. m∠2 = 26°
b. m∠2 = 78°
c. m∠2 = 36°
d. m∠2 = 66°

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle1+\angle2+\angle3 = 180^{\circ}\).
Substitute \(\angle1 = 3x\), \(\angle2=x + 10\), and \(\angle3=2x + 14\) into the equation:
\(3x+(x + 10)+(2x + 14)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+x+2x)+(10 + 14)=180\)
\(6x+24 = 180\)

Step3: Solve for \(x\)

Subtract 24 from both sides: \(6x=180 - 24\)
\(6x=156\)
Divide both sides by 6: \(x=\frac{156}{6}=26\)

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

Since \(\angle2=x + 10\) and \(x = 26\), then \(\angle2=26+10\)
\(\angle2 = 36^{\circ}\)

Answer:

C. \(m\angle2 = 36^{\circ}\)