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: Identify angle - relationship

Since line m || line n, ∠2 and ∠3 are corresponding angles, so m∠2 = m∠3.

Step2: Set up the equation

Set 5x - 14=3x + 10.

Step3: Solve the equation for x

Subtract 3x from both sides: 5x-3x - 14=3x-3x + 10, which gives 2x-14 = 10. Then add 14 to both sides: 2x-14 + 14=10 + 14, so 2x=24. Divide both sides by 2: x = 12.

Step4: Find m∠3

Substitute x = 12 into the expression for m∠3. m∠3=3x + 10=3×12 + 10=36 + 10=46°.

Step5: Use linear - pair relationship

∠1 and ∠3 form a linear - pair. So m∠1+m∠3 = 180°.

Step6: Solve for m∠1

m∠1=180°-m∠3. Substitute m∠3 = 46° into the equation, we get m∠1=180 - 46=134°.

Answer:

m∠1 = 134°