Question

Angles are created when lines a and b are cut by a transversal, t. These angles are labeled in the diagram.

Select the claim that is true about lines a and b for all cases.


A

If lines a and b are cut by a transversal, t, such that m∠1=m∠5, m∠2=m∠6, m∠3=m∠7, and m∠4=m∠8, then the lines must be parallel.


B

If lines a and b are cut by a transversal, t, such that m∠1+m∠5=180°, m∠2+m∠6=180°, m∠3+m∠7=180°, and m∠4+m∠8=180°, then the lines must be parallel.


C

If lines a and b are cut by a transversal, t, such that m∠1=m∠5, m∠2=m∠6, m∠3=m∠7, and m∠4=m∠8, then the lines must be perpendicular.


D

If lines a and b are cut by a transversal, t, such that m∠1+m∠5=90°, m∠2+m∠6=90°, m∠3+m∠7=90°, and m∠4+m∠8=90°, then the lines must be perpendicular.


PLEASE ANSWER FAST

Answer 1

<7= 101

<8= 101

Hence, <1= 101, <2=79, <3= 101, <4= 101, <5= 79, <6= 79, <7= 101, and <8= 101

Explanation:

3x + 19 = 5x - 29 ( opposite angles)

2x = 48

x = 24

Hence, the value N = 2y

< 2 = 3x + 7 ( Verticaly opposite angles).

<2 = 3 (24) + 7

<2 = 79

<1 + <2 = 180

<1 = 180 - <2 = 180 - 79 = 101

<1 = 101

<1 = 3 ( Opposite angle )

<3 = 101

<5 = 3x + 7 ( Adjacent angles )

<5 = 79

<4 + <5 = 180

<4 = 101

<6 = <5 ( Verticaly opposite angles )

<6 = 79

<7 = <4 ( Adjacent Angles )

< 8 = 4x + 5

<7 = 101

<8 = 101

Hence, <1 = 101, <2 = 79, <3 = 101, <4 = 101, <5 = 79, <6 = 79, <7 = 101, <8 = 101