Question

in exercises 6 and 7, for what value of x is l || m? which theorem or postulate justifies your answer in each case? 6. (3x - 63)° (2x + 2)° 7. (6x + 24)° (2x + 20)° envision florida b.e.s.t. geometry • teaching resources

Explanation:

Step1: Identify angle - relationship

When two lines are parallel, corresponding angles are equal. In Exercise 6, the angles \((3x - 63)^{\circ}\) and \((2x + 2)^{\circ}\) are corresponding angles. So we set up the equation \(3x-63 = 2x + 2\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3x-2x-63=2x - 2x+2\), which simplifies to \(x-63 = 2\). Then add 63 to both sides: \(x=2 + 63\), so \(x = 65\).

Step3: For Exercise 7

The angles \((6x + 24)^{\circ}\) and \((2x+20)^{\circ}\) are same - side interior angles. When two lines are parallel, same - side interior angles are supplementary, so \((6x + 24)+(2x+20)=180\).

Step4: Combine like terms

\(6x+2x+24 + 20=180\), which gives \(8x+44 = 180\).

Step5: Solve for \(x\)

Subtract 44 from both sides: \(8x+44-44=180 - 44\), so \(8x=136\). Then divide both sides by 8: \(x=\frac{136}{8}=17\).

Answer:

For Exercise 6, \(x = 65\). For Exercise 7, \(x = 17\).