Question

consider the diagram and angle measures shown below. m∠1=(3x + 25)°. m∠2=(7x + 5)°. m∠3=(-2x + 70)°. what is the value of m∠3?

Explanation:

Step1: Use property of parallel lines

Since \(l\parallel m\), \(\angle1\) and \(\angle2\) are corresponding - angles, so \(m\angle1 = m\angle2\).
\((3x + 25)=(7x + 5)\)

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(3x+25-3x=7x + 5-3x\), which gives \(25 = 4x+5\).
Subtract 5 from both sides: \(25 - 5=4x+5 - 5\), so \(20 = 4x\).
Divide both sides by 4: \(\frac{20}{4}=\frac{4x}{4}\), then \(x = 5\).

Step3: Find the measure of \(\angle3\)

Substitute \(x = 5\) into the expression for \(m\angle3\).
\(m\angle3=-2x + 70\).
\(m\angle3=-2\times5 + 70\).
\(m\angle3=-10 + 70\).
\(m\angle3 = 60^{\circ}\)

Answer:

\(60^{\circ}\)