Question

multiple choice
identify the choice that best completes the statement or answers the question.

1. in the diagram $a \parallel b$. use the diagram to answer the question.

(diagram not scale.)

if $m\angle2=(2x)^\circ$ and $m\angle5=(2x + 20)^\circ$, what is the measure of $\angle5$
a. $68^\circ$ b. $100^\circ$ c. $0^\circ$ d. $40^\circ$

1. is line $l$ parallel to line $m$? explain.

not drawn to scale
a. yes; alternate interior angles are congruent. b. yes; corresponding angles are congruent.
c. no; corresponding angles are not congruent. d. no; alternate interior angles are not congruent

Explanation:

Question 16

Step1: Identify angle relationship

Since $a \parallel b$, $\angle 2$ and $\angle 5$ are same-side interior angles, so they are supplementary: $m\angle 2 + m\angle 5 = 180^\circ$

Step2: Substitute given expressions

Substitute $m\angle 2=(2x)^\circ$ and $m\angle 5=(2x+20)^\circ$:
$$2x + (2x + 20) = 180$$

Step3: Solve for $x$

Simplify and solve:
$$4x + 20 = 180$$
$$4x = 180 - 20 = 160$$
$$x = \frac{160}{4} = 40$$

Step4: Calculate $m\angle 5$

Substitute $x=40$ into $m\angle 5=(2x+20)^\circ$:
$$m\angle 5 = 2(40) + 20 = 100$$

To check if lines $l$ and $m$ are parallel, examine the corresponding angles. The given angles are $116^\circ$ and $118^\circ$, which are not congruent. For lines to be parallel, corresponding angles must be congruent.

Answer:

b. $100^\circ$

---

Question 17