Question

#1.) which of the following statements are true based on the figure below when l || m?
i: ∠1 and ∠5 are corresponding angles
ii: ∠8 and ∠1 are alternate exterior angles
iii: ∠6 and ∠2 are same side exterior angles
a.) i only
b.) i and ii
c.) ii and iii only
d.) iii only
**#2.) determine the sum of x and y below.
a.) 12
b.) 19
c.) 35
d.) 42
#3.) in the figure below, the m∠3 = 27° and the m∠5 = 152°. which of the following is not true?
i: m∠2 = 27°
ii: m∠6 = 28°
iii: a || b
iv: a || b
a.) ii only
b.) iii only
c.) i and ii
d.) ii and iv

Explanation:

Step1: Analyze statement I

Corresponding angles are in the same relative position. $\angle1$ and $\angle5$ are in the same relative position with respect to the parallel lines $l$ and $m$ and the transversal $n$. So, statement I is true.

Step2: Analyze statement II

Alternate exterior angles are non - adjacent exterior angles on opposite sides of the transversal. $\angle8$ and $\angle1$ are non - adjacent exterior angles on opposite sides of the transversal $n$. So, statement II is true.

Step3: Analyze statement III

Same - side exterior angles are exterior angles on the same side of the transversal. $\angle6$ is an interior angle. So, statement III is false.

Answer:

B. I and II