Question

name falemch
math 20 foundations chapter 2 exam a
/30
multiple choice
identify the choice that best completes the statement or answers the question.

1. which statement about the angles in this diagram is false?
2. which angle property proves ∠dab = 120°?
3. in which diagrams are two lines parallel?
4. which are the correct measures of the indicated angles?
5. which are the correct measures for ∠yxz and ∠xzy?
6. which are the correct measures for ∠dce and ∠cab?

Explanation:

Step1: Analyze question 1

Use angle - relationship rules for parallel lines. $\angle e$ and $\angle f$ are vertical angles, $\angle a$ and $\angle b$ are corresponding angles, $\angle d$ and $\angle c$ are vertical angles. $\angle f$ and $\angle a$ are not equal in general. So the false statement is $\angle f=\angle a$.

Step2: Analyze question 2

$\angle DAB$ and the $120^{\circ}$ angle are vertically - opposite angles. Vertically opposite angles are equal.

Step3: Analyze question 3

For parallel lines, corresponding angles are equal. In choice 1, the corresponding angles are equal ($109^{\circ}$ and $109^{\circ}$), in choice 2, the corresponding angles are equal ($58^{\circ}$ and $58^{\circ}$), in choice 3, the corresponding angles are equal ($67^{\circ}$ and $67^{\circ}$). So choices 1, 2, and 3 have parallel lines.

Step4: Analyze question 4

Using the property of corresponding and supplementary angles for parallel lines. If one angle is $46^{\circ}$, its corresponding angle is $46^{\circ}$ and the supplementary angle to the $46^{\circ}$ angle is $134^{\circ}$. So $\angle w = 134^{\circ},\angle x=46^{\circ},\angle y = 46^{\circ}$.

Step5: Analyze question 5

In a triangle, the sum of interior angles is $180^{\circ}$. $\angle YXZ=180^{\circ}-(36^{\circ}+117^{\circ}) = 27^{\circ}$ is wrong. $\angle YXZ = 180^{\circ}-(36^{\circ}+91^{\circ})=53^{\circ}$ and $\angle XZY = 91^{\circ}$.

Step6: Analyze question 6

$\angle DCE$ and the $143^{\circ}$ angle are supplementary, so $\angle DCE=180 - 143=37^{\circ}$. In the triangle with $\angle CAB$, using the angle - sum property of a triangle, $\angle CAB=180-(24^{\circ}+37^{\circ}) = 119^{\circ}$.

Answer:

1. d
2. a
3. a
4. b
5. b
6. b