Lesson: Applications of the Relations between Lines and Angles

In this lesson, we will learn how to identify special pairs of angles and point them out and how to solve problems based on the relation between lines and angles.

Sample Question Videos

  • 01:34

Worksheet: Applications of the Relations between Lines and Angles • 25 Questions • 1 Video

Q1:

From the figure, determine 𝑚 𝐴 𝐸 𝐶 .

Q2:

Suppose that 𝑀 𝐸 bisects 𝐴 𝑀 𝐷 , find 𝑚 𝐸 𝑀 𝐶 .

Q3:

In the figure, lines 𝐴 𝐶 and 𝐷 𝐵 meet at 𝑂 . Find 𝐴 𝑂 𝑋 .

Q4:

Given that 𝐴 , 𝐵 , 𝐶 , and 𝐷 are collinear, find 𝑚 𝐷 𝐶 𝑌 .

Q5:

Given the following figure, find the value of 𝑥 .

Q6:

Find 𝑚 𝑦 given that 𝑚 𝑥 = 2 9 and 𝑚 𝐴 𝐵 𝐶 = 1 3 9 .

Q7:

Every time the turtle turns, he turns 6 0 . If he ends up turning in a full circle, how many 6 0 turns did he make?

Q8:

Use < , = , or > to fill in the blank: 𝑚 𝑋 𝐶 𝐵 𝑚 𝐴 𝐶 𝑌 .

Q9:

In the figure below, 𝑚 𝐵 𝐴 𝐶 = 3 0 . If 𝐴 𝐶 is an angle bisector, what is 𝑚 𝐵 𝐴 𝐷 ?

Q10:

Find 𝑚 𝑥 if 𝑚 𝑦 = 4 8 and 𝑚 𝐽 𝐾 𝐿 = 1 1 2 .

Q11:

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

Q12:

Find the value of 𝑥 .

Q13:

If 𝑚 𝐵 𝑀 𝐶 = 2 𝑚 𝐴 𝑀 𝐵 , find 𝑚 𝐴 𝑀 𝐷 .

Q14:

Are 1 and 2 adjacent angles?

Q15:

Find the value of 𝑥 .

Q16:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Q17:

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

Q18:

Determine 𝑚 𝐴 𝐵 𝐸 .

Q19:

Find 𝑚 𝐶 𝐵 𝐸 .

Q20:

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

Q21:

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

Is there a translation that can map to ?

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

What is true of angles are and ?

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

Q22:

Using the information in the figure, determine 𝑚 𝐴 𝐹 𝐸 .

Q23:

In the figure below, find 𝑚 𝐴 𝐵 𝐶 .

Q24:

𝐺 , 𝐸 , and 𝐶 are accumulative angles at a point. If 𝑚 𝐺 = 5 5 and 𝑚 𝐸 = 1 6 5 , find 𝑚 𝐶 .

Q25:

The figure shows a pair of parallel lines with a transversal drawn through them.

What name is given to the pairs of green and red angles highlighted in the figure?

What name is given to the pairs of blue and orange angles highlighted in the figure?

What do you notice regarding the sizes of two alternate angles?

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