Question

6.) given: line m || line n, m∠2 = 5x - 14, and m∠3 = 3x + 10. prove: m∠1 = 134°. statements reasons 1.) 2.) 3.) 4.) 5.) 6.) 7.) 8.) 9.) 10.) 11.) 12.)

Explanation:

Step1: Use corresponding - angles property

Since line \(m\parallel\) line \(n\), \(\angle2\) and \(\angle3\) are corresponding angles, so \(m\angle2 = m\angle3\). Then \(5x - 14=3x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(5x-3x - 14=3x-3x + 10\), which simplifies to \(2x-14 = 10\). Then add 14 to both sides: \(2x-14 + 14=10 + 14\), getting \(2x=24\). Divide both sides by 2: \(x = 12\).

Step3: Find \(m\angle2\)

Substitute \(x = 12\) into the expression for \(m\angle2\): \(m\angle2=5x - 14=5\times12-14=60 - 14 = 46^{\circ}\).

Step4: Use linear - pair property

\(\angle1\) and \(\angle2\) form a linear - pair. Since the sum of angles in a linear - pair is \(180^{\circ}\), \(m\angle1=180^{\circ}-m\angle2\).

Step5: Calculate \(m\angle1\)

\(m\angle1 = 180 - 46=134^{\circ}\).

Answer:

The proof is completed as above to show \(m\angle1 = 134^{\circ}\).