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: Set up the equation

When \(f\parallel g\), the angles \((14x + 8)^{\circ}\) and \((6x+12)^{\circ}\) are congruent (corresponding angles). So, \(14x + 8=6x + 12\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(14x-6x + 8=6x-6x + 12\), which gives \(8x+8 = 12\).
Subtract \(8\) from both sides: \(8x+8 - 8=12 - 8\), so \(8x=4\).
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. \(m\angle TUV=15^{\circ}\)