Question

1. what type of lines are coplanar and do not intersect?

a parallel
c segments
b perpendicular
d transversal
for items 2 - 5, lines ( r ) and ( m ) are intersected by transversal ( t ). ( r parallel m )

1. select all the angles that are supplementary to ( angle 1 ).

a ( angle 3 )
c ( angle 5 )
e ( angle 7 )
b ( angle 4 )
d ( angle 6 )
f ( angle 8 )

1. select all the angles that are congruent to ( angle 5 ).

a ( angle 1 )
c ( angle 3 )
e ( angle 7 )
b ( angle 2 )
d ( angle 4 )
f ( angle 8 )

1. complete the following plan to prove that ( angle 3 cong angle 6 ).

use the same - side interior angles postulate to show that ( angle 3 ) is supplementary to
show ( angle 6 ) and are because they form a
since ( angle 3 ) and ( angle 6 ) are to the same angle, they are congruent to each other.

1. if ( m angle 2 = 112 ), what is ( m angle 7 )?

( m angle 7=)

1. select all the true statements given the figure.

a ( m angle 4 = m angle 2 )
b ( m angle 4 = m angle 1 + m angle 2 )
c ( m angle 4 = 180 - m angle 3 )
d ( m angle 4 = m angle 1 + m angle 2 + m angle 3 )
e ( m angle 4 = m angle 3 + m angle 1 )
for items 7 - 9, use the figure shown.

1. what is ( x )?

a 28
c 136
b 44
d 224

1. what is ( y )?

( y=)

1. select all the true statements.

a ( x = y )
d ( x + z = 180 )
b ( x + y = 180 )
e ( y + z = 180 )
c ( y = z )

Explanation:

Step1: Find \(m\angle7\)

Since \(l\parallel m\), \(\angle2\) and \(\angle7\) are alternate - exterior angles. Alternate - exterior angles are congruent when two parallel lines are cut by a transversal. So \(m\angle7 = m\angle2\). Given \(m\angle2=112\), then \(m\angle7 = 112\).

Step2: Analyze question 6

• Option A: \(\angle4\) and \(\angle2\) are not congruent.
• Option B: By the exterior - angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So \(m\angle4=m\angle1 + m\angle2\).
• Option C: Since \(\angle3\) and \(\angle4\) are supplementary (\(\angle3+\angle4 = 180^{\circ}\)), then \(m\angle4=180 - m\angle3\).
• Option D: \(m\angle4=m\angle1 + m\angle2

eq m\angle1 + m\angle2 + m\angle3\).

• Option E: \(m\angle4=m\angle1 + m\angle2

eq m\angle3 + m\angle1\).

Step3: Analyze question 7

Using the exterior - angle theorem for the triangle, \(x=54 + 82\).

$$x=136$$

Step4: Analyze question 8

\(y\) and \(x\) are supplementary (they form a linear pair). So \(y = 180 - x\). Since \(x = 136\), then \(y=180 - 136=44\).

Step5: Analyze question 9

• Option A: \(x = 136\) and \(y = 44\), so \(x

eq y\).

• Option B: \(x + y=136 + 44=180\).
• Option C: \(y = 44\) and \(z\) (if we consider the triangle, \(z = 54\)), so \(y

eq z\).

• Option D: \(x\) and \(z\) are not supplementary.
• Option E: \(y\) and \(z\) are not supplementary.

Answer:

1. A
2. A, B
3. A, E
4. \(\angle5\); \(\angle5\); supplementary; linear pair; supplementary to the same
5. \(112\)
6. B, C
7. C
8. \(44\)
9. B