Lesson: Using Angle Relationships to Solve Algebraic Expressions

In this lesson, we will learn how to use angle relationships to solve some algebraic expressions.

Sample Question Videos

  • 03:33

Worksheet: Using Angle Relationships to Solve Algebraic Expressions • 20 Questions • 1 Video

Q1:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

Find the value of 𝑥 .

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 .

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 .

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q4:

Given that is a rectangle, , and , find .

Q5:

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

Q6:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

Find the value of 𝑥 .

Q7:

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 .

Solve for 𝑥 .

Q8:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

Find the value of 𝑥 .

Q9:

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

Q10:

Quadrilateral is a rectangle. If and , find .

Q11:

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 .

Solve for 𝑥 .

Q12:

Find 𝑚 𝐷 𝐶 𝐸 .

Q13:

If , , and , find the size of each angle.

Q14:

In the figure below, 𝐾 𝐽 and 𝐾 𝑀 are opposite rays, and 𝐾 𝑁 bisects 𝐽 𝐾 𝐿 . If 𝑚 𝐽 𝐾 𝑁 = ( 5 𝑥 7 ) and 𝑚 𝑁 𝐾 𝐿 = ( 4 𝑥 + 4 ) , find 𝑚 𝐽 𝐾 𝑁 .

Q15:

In the given figure, and are opposite rays, and bisects . If and , find .

Q16:

In the given figure, find the values of and .

Q17:

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

Form an equation that will allow you to calculate 𝑥 .

Find the value of 𝑥 .

Q18:

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 .

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q19:

Find the values of and so that and are perpendicular.

Q20:

In this figure, and form a linear pair. If , , and , determine .

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