Question

find the value of x that would make f||g. then find the measures of the two angles. 3 pts each

1. x=
2. m∠wyz=
3. m∠tuv=

Explanation:

Step1: Use the property of alternate interior angles

If \(f\parallel g\), then \((14x + 8)^{\circ}=(6x + 12)^{\circ}\) (alternate - interior angles are equal).

$$14x+8 = 6x + 12$$

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides:

$$14x-6x+8=6x - 6x+12$$

$$8x+8 = 12$$

Subtract \(8\) from both sides:

$$8x+8 - 8=12 - 8$$

$$8x=4$$

Divide both sides by \(8\):

$$x=\frac{4}{8}=\frac{1}{2}$$

Step3: Find \(m\angle WYZ\)

Substitute \(x = \frac{1}{2}\) into \(14x + 8\):

$$14\times\frac{1}{2}+8=7 + 8=15$$

Step4: Find \(m\angle TUV\)

Substitute \(x=\frac{1}{2}\) into \(6x + 12\):

$$6\times\frac{1}{2}+12=3 + 12=15$$

Answer:

1. \(x=\frac{1}{2}\)
2. \(m\angle WYZ = 15^{\circ}\)
3. \(m\angle TUV=15^{\circ}\)