Question

geometry
parallel lines & transversal practice
find the measure of the indicated angle that makes lines u and v parallel.
1)
2)

solve for x. name the angle relationship(s) used to set up your equation.
3)
4)

Explanation:

Step1: Solve Q1 (Alternate Exterior Angles)

For parallel lines, alternate exterior angles are equal.
$\text{Angle measure} = 116^\circ$

Step2: Solve Q2 (Alternate Interior Angles)

For parallel lines, alternate interior angles are equal.
$\text{Angle measure} = 74^\circ$

Step3: Solve Q3 (Same-Side Interior Angles)

Same-side interior angles are supplementary. Set up equation:
$$(8x - 10) + 110 = 180$$
Simplify:
$$8x + 100 = 180$$
$$8x = 80$$
$$x = 10$$

Step4: Solve Q4 (Corresponding Angles)

Corresponding angles are equal. Set up equation:
$$11x = 5 + 10x$$
Simplify:
$$11x - 10x = 5$$
$$x = 5$$

Answer:

1. $\boldsymbol{116^\circ}$
2. $\boldsymbol{74^\circ}$
3. $\boldsymbol{x=10}$ (Same-Side Interior Angles)
4. $\boldsymbol{x=5}$ (Corresponding Angles)