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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 π‘š ∠ 𝑦 given that π‘š ∠ π‘₯ = 2 9 ∘ and π‘š ∠ 𝐴 𝐡 𝐢 = 1 3 9 ∘ .

Q8:

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?

Q9:

Use , , or to fill in the blank: .

  • A
  • B
  • C

Q10:

In the figure below, π‘š ∠ 𝐡 𝐴 𝐢 = 3 0 ∘ . If  𝐴 𝐢 is an angle bisector, what is π‘š ∠ 𝐡 𝐴 𝐷 ?

Q11:

Find π‘š ∠ π‘₯ if π‘š ∠ 𝑦 = 4 8 ∘ and π‘š ∠ 𝐽 𝐾 𝐿 = 1 1 2 ∘ .

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:

Are ∠ 1 and ∠ 2 adjacent angles?

  • Ano
  • Byes

Q16:

Find the value of .

  • A
  • B
  • C
  • D

Q17:

Answer the questions for the given figure.

Find the value of π‘₯ .

Find the value of 𝑦 .

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 π‘š ∠ 𝐴 𝐡 𝐹 = 3 8 ∘ and π‘š ∠ 𝐹 𝐷 𝐸 = 5 3 ∘ , find the measure of each numbered angle.

  • A π‘š ∠ 1 = 5 2 ∘ , π‘š ∠ 2 = 3 7 ∘ , π‘š ∠ 3 = 5 3 ∘
  • B π‘š ∠ 1 = 3 8 ∘ , π‘š ∠ 2 = 5 3 ∘ , π‘š ∠ 3 = 3 7 ∘
  • C π‘š ∠ 1 = 3 8 ∘ , π‘š ∠ 2 = 3 7 ∘ , π‘š ∠ 3 = 5 3 ∘
  • D π‘š ∠ 1 = 5 2 ∘ , π‘š ∠ 2 = 5 3 ∘ , π‘š ∠ 3 = 3 7 ∘
  • E π‘š ∠ 1 = 3 8 ∘ , π‘š ∠ 2 = 5 3 ∘ , π‘š ∠ 3 = 5 3 ∘

Q22:

In the given figure, βƒ–     βƒ— 𝐴 𝐢 and βƒ–     βƒ— 𝐡 𝐷 are parallel lines and βƒ–     βƒ— 𝐴 𝐡 is a transversal.

Is there a translation that can map βƒ–     βƒ— 𝐴 𝐢 to βƒ–     βƒ— 𝐡 𝐷 ?

  • Ayes
  • Bno

What, therefore, is true of the corresponding angles π‘Ž and 𝑏 ?

  • AThey have equal measure.
  • BThey are right angles.
  • CThey are suplementary.
  • 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 π‘Ž and 𝑐 ?

  • 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 π‘š ∠ 𝐴 𝐡 𝐢 .

  • A 6 7 ∘
  • B 4 6 ∘
  • C 1 3 4 ∘

Q25:

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

  • A
  • B
  • C
  • D