**#3.) if ( m angle age = (125)^{circ} ) and ( m angle bgh = (125)^{circ} ), explain how you know that ( overline{ab} ) is not parallel to ( cd ).
#4.) use the diagram below to answer questions a., b.,
and c.
a) **name one angle that is congruent to ( angle 2 ) that
makes lines ( a ) and ( b ) parallel
b) using the angle from part a), explain why ( a ) and ( b ) are parallel.

c) *name one angle that is supplementary to ( angle 2 ) that makes lines ( a ) and ( b ) parallel. explain why ( a ) and ( b ) are parallel.

d) **name one angle that is supplementary to ( angle 2 ) that does not make ( a ) and ( b ) parallel. explain why ( a ) and ( b ) are not parallel.

#5.) (sat question) in the figure below, what is the value of ( y )? think: triangle sum theorem and linear pairs!

Question

**#3.) if ( m angle age = (125)^{circ} ) and ( m angle bgh = (125)^{circ} ), explain how you know that ( overline{ab} ) is not parallel to ( cd ).
#4.) use the diagram below to answer questions a., b.,
and c.
a) **name one angle that is congruent to ( angle 2 ) that
makes lines ( a ) and ( b ) parallel
b) using the angle from part a), explain why ( a ) and ( b ) are parallel.

c) *name one angle that is supplementary to ( angle 2 ) that makes lines ( a ) and ( b ) parallel. explain why ( a ) and ( b ) are parallel.

d) **name one angle that is supplementary to ( angle 2 ) that does not make ( a ) and ( b ) parallel. explain why ( a ) and ( b ) are not parallel.

#5.) (sat question) in the figure below, what is the value of ( y )? think: triangle sum theorem and linear pairs!

Accepted Answer

### #4
#### a)
# Brief Explanations:
Corresponding angles are congruent when lines are parallel. $\angle6$ is a corresponding angle to $\angle2$.
# Answer:
$\angle6$

#### b)
# Brief Explanations:
By the Corresponding Angles Postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Since $\angle2\cong\angle6$, lines $a$ and $b$ are parallel.
# Answer:
By the Corresponding Angles Postulate,  if $\angle2\cong\angle6$, then $a\parallel b$.

#### c)
# Brief Explanations:
$\angle8$ is supplementary to $\angle2$ ($\angle2+\angle8 = 180^{\circ}$ as they are same - side interior angles). By the Same - Side Interior Angles Theorem, if two lines are cut by a transversal and the same - side interior angles are supplementary, then the lines are parallel.
# Answer:
$\angle8$; By the Same - Side Interior Angles Theorem, if $\angle2+\angle8 = 180^{\circ}$, then $a\parallel b$.

#### d)
# Brief Explanations:
$\angle4$ is supplementary to $\angle2$ ($\angle2+\angle4=180^{\circ}$ as they are a linear pair). But $\angle4$ and $\angle2$ are on the same line $a$ (they form a linear pair on line $a$), not related to the parallelism of $a$ and $b$.
# Answer:
$\angle4$; $\angle2$ and $\angle4$ form a linear pair on line $a$, not related to the parallelism of $a$ and $b$.

### #5
# Explanation:
## Step1: Find the third angle of the left - hand triangle
Using the Triangle Sum Theorem ($\angle A+\angle B+\angle C = 180^{\circ}$). Let the third angle of the left - hand triangle be $x$. Then $x+60^{\circ}+50^{\circ}=180^{\circ}$, so $x = 180^{\circ}-(60^{\circ}+50^{\circ})=70^{\circ}$.
## Step2: Use the exterior angle property (or linear pair and triangle sum)
The angle adjacent to $x$ (let's call it $z$) forms a linear pair with $x$, so $z = 180^{\circ}-x=110^{\circ}$. Then, for the right - hand triangle, using the Triangle Sum Theorem: $y + z+40^{\circ}=180^{\circ}$. Substitute $z = 110^{\circ}$ into the equation: $y+110^{\circ}+40^{\circ}=180^{\circ}$.
## Step3: Solve for $y$
$y=180^{\circ}-(110^{\circ}+40^{\circ})$.
# Answer:
$y = 30$

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QUESTION IMAGE

Question

Explanation:

#4

a)

Answer:

b)