Worksheet: Using Angle Relationships to Solve Algebraic Expressions

In this worksheet, we will practice using angle relationships to solve some algebraic expressions.

Q1:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

  • A 1 5 𝑥 + 5 0 = 9 0 ( 5 𝑥 + 6 0 )
  • B 1 5 𝑥 + 5 0 = 1 8 0 ( 5 𝑥 + 6 0 )
  • C 1 5 𝑥 + 5 0 = 1 8 0 + 5 𝑥 + 6 0
  • D 1 5 𝑥 + 5 0 = 5 𝑥 + 6 0
  • E 1 5 𝑥 + 5 0 = 9 0 + 5 𝑥 + 6 0

Find the value of 𝑥 .

  • A 𝑥 = 1
  • B 𝑥 = 1 9
  • C 𝑥 = 2
  • D 𝑥 = 1 7
  • E 𝑥 = 1 0

Q2:

In the given diagram, 𝑚 𝐴 𝑋 𝐵 = ( 1 2 𝑥 4 ) and 𝑚 𝐶 𝑋 𝐷 = ( 8 𝑥 + 1 2 ) . Find the value of 𝑥 .

  • A 𝑥 = 2
  • B 𝑥 = 8
  • C 𝑥 = 1 6
  • D 𝑥 = 4
  • E 𝑥 = 7

Q3:

In the given diagram, 𝐴 𝐵 and 𝐶 𝐷 are straight lines. Answer the following questions.

Form an equation that will allow you to calculate 𝑥 .

  • A 5 𝑥 + 2 = 9 0
  • B 1 1 𝑥 + 2 = 1 8 0
  • C 6 𝑥 = 9 0
  • D 1 1 𝑥 + 2 = 9 0
  • E 6 𝑥 = 1 8 0

Find the value of 𝑥 .

  • A 𝑥 = 8
  • B 𝑥 = 1 5
  • C 𝑥 = 1 8
  • D 𝑥 = 1 6
  • E 𝑥 = 3 0

Find the value of 𝑦 .

  • A 𝑦 = 1 3 8
  • B 𝑦 = 4 2
  • C 𝑦 = 4 8
  • D 𝑦 = 3 0
  • E 𝑦 = 1 3 2

Find the value of 𝑧 .

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

Q4:

From the intersecting lines in the figure, determine the value of 𝑥 .

Q5:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

  • A 7 𝑥 = 5 6
  • B 7 𝑥 = 6 8
  • C 7 𝑥 = 1 5 8
  • D 7 𝑥 = 1 1 2
  • E 7 𝑥 = 2 2

Find the value of 𝑥 .

  • A 𝑥 = 1 6
  • B 𝑥 = 3 5
  • C 𝑥 = 8
  • D 𝑥 = 1 0
  • E 𝑥 = 3

Q6:

In the given diagram, 𝐴 𝐵 𝐶 is a right angle and 𝑚 𝐴 𝐵 𝐷 is twice 𝑚 𝐷 𝐵 𝐶 . Let 𝑚 𝐷 𝐵 𝐶 = 𝑥 .

Form an equation that will allow you to calculate 𝑥 .

  • A 4 𝑥 = 9 0
  • B 2 𝑥 = 9 0
  • C 2 𝑥 = 1 8 0
  • D 3 𝑥 = 9 0
  • E 3 𝑥 = 1 8 0

Solve for 𝑥 .

  • A 𝑥 = 3 0
  • B 𝑥 = 6 0
  • C 𝑥 = 9 0
  • D 𝑥 = 4 5
  • E 𝑥 = 2 2 . 5

Q7:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

  • A 3 𝑥 + 4 6 = 9 0
  • B 3 𝑥 + 4 4 = 9 0
  • C 3 𝑥 + 2 = 4 6
  • D 3 𝑥 + 4 8 = 9 0
  • E 3 𝑥 + 4 8 = 4 6

Find the value of 𝑥 .

  • A 𝑥 = 1 4
  • B 𝑥 = 1 6
  • C 𝑥 = 2
  • D 𝑥 = 4 2
  • E 𝑥 = 3 0

Q8:

If 𝐸 𝐶 is an altitude of 𝐴 𝐸 𝐷 , 𝑚 𝜃 = ( 5 𝑥 + 2 ) , and 𝑚 𝜙 = ( 3 𝑥 + 8 ) , find 𝑚 𝜃 .

Q9:

In the given diagram, 𝐴 𝐷 is a straight line, 𝑚 𝐴 𝐵 𝐶 = ( 4 𝑥 + 1 2 ) , and 𝑚 𝐷 𝐵 𝐶 = ( 6 𝑥 + 8 ) .

Form an equation that will allow you to calculate 𝑥 .

  • A 4 𝑥 + 1 2 = 9 0
  • B 1 0 𝑥 + 2 0 = 9 0
  • C 2 𝑥 + 2 0 = 1 8 0
  • D 1 0 𝑥 + 2 0 = 1 8 0
  • E 2 𝑥 + 2 0 = 9 0

Solve for 𝑥 .

  • A 𝑥 = 1 6
  • B 𝑥 = 8
  • C 𝑥 = 1 9 . 5
  • D 𝑥 = 7
  • E 𝑥 = 3 5

Q10:

Find 𝑚 𝐷 𝐶 𝐸 .

Q11:

In the given figure, find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 1 4 , 𝑦 = 3 8
  • B 𝑥 = 1 5 , 𝑦 = 3 7
  • C 𝑥 = 8 9 , 𝑦 = 9 1
  • D 𝑥 = 1 5 , 𝑦 = 3 8
  • E 𝑥 = 8 9 , 𝑦 = 1

Q12:

In the given diagram, 𝐴 𝐵 is a straight line. Answer the following questions.

Form an equation that will allow you to calculate 𝑥 .

  • A 3 𝑥 = 3 0
  • B 3 𝑥 + 3 0 = 1 8 0
  • C 3 𝑥 + 3 0 = 2 7 0
  • D 3 𝑥 + 3 0 = 9 0
  • E 3 𝑥 + 3 0 = 3 6 0

Find the value of 𝑥 .

  • A 𝑥 = 2 0
  • B 𝑥 = 8 0
  • C 𝑥 = 1 0
  • D 𝑥 = 5 0
  • E 𝑥 = 1 1 0

Q13:

In the given diagram, 𝐴 𝐵 and 𝐶 𝐷 are straight lines. Answer the following questions.

Form an equation that will allow you to calculate 𝑥 .

  • A 1 0 𝑥 + 2 0 = 6 0
  • B 1 0 𝑥 + 2 0 = 1 8 0
  • C 1 0 𝑥 + 1 0 = 9 0
  • D 1 0 𝑥 + 2 0 = 9 0
  • E 1 0 𝑥 + 1 0 = 1 8 0

Find the value of 𝑥 .

  • A 𝑥 = 7
  • B 𝑥 = 8
  • C 𝑥 = 4
  • D 𝑥 = 1 6
  • E 𝑥 = 1 7

Find the value of 𝑦 .

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

Find the value of 𝑧 .

  • A 𝑧 = 1 2 0
  • B 𝑧 = 9 0
  • C 𝑧 = 4 5
  • D 𝑧 = 6 0
  • E 𝑧 = 3 0

Q14:

Find the values of 𝑥 and 𝑦 so that 𝑃 𝑅 and 𝑆 𝑄 are perpendicular.

  • A 𝑥 = 3 0 , 𝑦 = 2 9
  • B 𝑥 = 8 , 𝑦 = 2 9
  • C 𝑥 = 5 , 𝑦 = 6 5
  • D 𝑥 = 5 , 𝑦 = 2 9
  • E 𝑥 = 2 5 , 𝑦 = 6 5

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