# Worksheet: Applications on the Relations between Lines and Angles

Q1:

In the figure, lines and meet at . Find .

• A
• B
• C
• D

Q2:

From the figure, determine .

• A
• B
• C
• D

Q3:

Given that , , , and are collinear, find .

• A
• B
• C
• D

Q4:

Given that , , , and are collinear, find .

• A
• B
• C
• D

Q5:

Suppose that bisects , find .

• A
• B
• C
• D

Q6:

Given the following figure, find the value of .

• A
• B
• C
• D
• E

Q7:

Find given that and .

Q8:

Every time the turtle turns, he turns . If he ends up turning in a full circle, how many turns did he make?

Q9:

Use , , or to fill in the blank: .

• A
• B
• C

Q10:

In the figure below, . If is an angle bisector, what is ?

Q11:

Find if and .

Q12:

In , and . Arrange the lengths of the sides of the triangle in descending order.

• A
• B
• C
• D
• E

Q13:

Find the value of .

• A50
• B22
• C46
• D25

Q14:

If , find .

• A
• B
• C
• D

Q15:

• Ano
• Byes

Q16:

Find the value of .

• A
• B
• C
• D

Q17:

Answer the questions for the given figure.

Find the value of .

Find the value of .

Q18:

If two lines intersect at a point, how many angles do they create?

• A5
• B2
• C3
• D4

Q19:

Determine .

• A
• B
• C
• D

Q20:

Find .

• A
• B
• C
• D

Q21:

Given that and , find the measure of each numbered angle.

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q22:

In the given figure, and are parallel lines and is a transversal.

Is there a translation that can map to ?

• Ayes
• Bno

What, therefore, is true of the corresponding angles and ?

• AThey have equal measure.
• BThey are right angles.
• CThey are suplementary.
• DThey are complementary.
• EThey are obtuse angles.

What is true of angles are and ?

• AThey are complementary angles and hence have a sum of .
• BThey are supplementary and hence have a sum of .
• CThey are vertically opposite and hence have equal measure.

What, therefore, is true of the alternate angles and ?

• AThey are of equal measure.
• BThey are complementary angles.
• CThey are supplementary angles.

Q23:

Using the information in the figure, determine .

• A
• B
• C
• D

Q24:

In the figure below, find .

• A
• B
• C

Q25:

, , and are accumulative angles at a point. If and , find .

• A
• B
• C
• D