Question

m∠1=(3x + 25)°
m∠2=(7x + 5)°
m∠3=(-2x + 70)°
what is the value of m∠3?
a. m∠3 = 40°
b. m∠3 = 52°
c. m∠3 = 60°
d. m∠3 = 80°

Explanation:

Step1: Use angle - relationship of parallel lines

Since \(l\parallel m\), \(\angle1\) and \(\angle2\) are supplementary angles (same - side interior angles), so \(m\angle1 + m\angle2=180^{\circ}\).
\((3x + 25)+(7x + 5)=180\)

Step2: Simplify the equation

Combine like - terms: \(3x+7x+25 + 5=180\), which gives \(10x+30 = 180\).
Subtract 30 from both sides: \(10x=180 - 30=150\).
Divide both sides by 10: \(x = 15\).

Step3: Find the value of \(m\angle3\)

Substitute \(x = 15\) into the expression for \(m\angle3\): \(m\angle3=-2x + 70\).
\(m\angle3=-2\times15+70=-30 + 70 = 40^{\circ}\)

Answer:

A. \(m\angle3 = 40^{\circ}\)