Worksheet: Applications of the Relations between Lines and Angles

In this worksheet, we will practice identifying special pairs of angles and pointing them out and solving problems based on the relation between lines and angles.

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 .

  • A 9 2
  • B 8 8
  • C 1 3 4
  • D 1 3 6

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 .

  • A 1 0 8
  • B 4 2
  • C 5 6
  • D 3 6
  • E 1 8

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 .

  • A =
  • B >
  • C <

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 𝐴 𝐵 𝐶 , 𝑚 𝐴 = 6 2 and 𝑚 𝐵 = 9 2 . Arrange the lengths of the sides of the triangle in descending order.

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

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?

  • Ano
  • Byes

Q15:

Find the value of 𝑥 .

  • A 1 1 9
  • B 1 0 6
  • C 6 5
  • D 6 1

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?

  • A5
  • B2
  • C3
  • D4

Q18:

Determine 𝑚 𝐴 𝐵 𝐸 .

Q19:

Find 𝑚 𝐶 𝐵 𝐸 .

Q20:

Given that 𝑚 𝐴 𝐵 𝐹 = 3 8 and 𝑚 𝐹 𝐷 𝐸 = 5 3 , find the measure of each numbered angle.

  • A 𝑚 1 = 5 2 , 𝑚 2 = 3 7 , 𝑚 3 = 5 3
  • B 𝑚 1 = 3 8 , 𝑚 2 = 5 3 , 𝑚 3 = 3 7
  • C 𝑚 1 = 3 8 , 𝑚 2 = 3 7 , 𝑚 3 = 5 3
  • D 𝑚 1 = 5 2 , 𝑚 2 = 5 3 , 𝑚 3 = 3 7
  • E 𝑚 1 = 3 8 , 𝑚 2 = 5 3 , 𝑚 3 = 5 3

Q21:

In the given figure, 𝐴 𝐶 and 𝐵 𝐷 are parallel lines and 𝐴 𝐵 is a transversal.

Is there a translation that can map 𝐴 𝐶 to 𝐵 𝐷 ?

  • Ayes
  • Bno

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

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

What is true of angles are 𝑏 and 𝑐 ?

  • AThey are complementary angles and hence have a sum of 9 0 .
  • BThey are supplementary and hence have a sum of 1 8 0 .
  • CThey are vertically opposite and hence have equal measure.

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

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

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?

  • Aalternate exterior angles
  • Bcorresponding angles
  • Cstraight angles
  • Dalternate interior angles

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

  • Astraight angles
  • Balternate interior angles
  • Ccorresponding angles
  • Dalternate exterior angles

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

  • AThey are supplementary.
  • BThey are complementary.
  • CThey are equal.

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