Unlocking Mystery Angles: Combining Geometry and Math

Mathematics Grades 7th Grade 1:42 Video
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Lesson Description

In this lesson, students will learn how to solve for unknown angles using adjacent angles and the combined measure of angles. We'll explore angle relationships and apply algebraic thinking to find missing angle measures.

Video Resource

Solving for an angle | Geometry | 4th grade | Khan Academy

Khan Academy

Duration: 1:42
Watch on YouTube

Key Concepts

  • Adjacent angles
  • Supplementary angles
  • Angle measurement
  • Solving for unknowns

Learning Objectives

  • Students will be able to identify adjacent angles.
  • Students will be able to calculate the measure of an unknown angle when given the measure of an adjacent angle and the combined angle.
  • Students will be able to apply algebraic thinking to solve for unknown angles.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic angle vocabulary (angle, degree, right angle, acute angle, obtuse angle). Briefly discuss the concept of adjacent angles and how they share a common vertex and side.
  • Video Viewing (5 mins)
    Play the Khan Academy video: "Solving for an angle | Geometry | 4th grade | Khan Academy". Instruct students to pay close attention to how the narrator identifies the angles and sets up the equation.
  • Guided Practice (10 mins)
    Work through a similar example problem on the board, modeling the process of identifying adjacent angles, setting up an equation, and solving for the unknown angle. For example: Angle PQR is 100 degrees. Angle PQS is 60 degrees. What is the measure of angle SQR?
  • Independent Practice (15 mins)
    Provide students with a worksheet containing similar problems to solve independently. Include problems with varying angle measures to challenge students. Encourage students to draw diagrams to help visualize the problem.
  • Wrap-up and Discussion (5 mins)
    Review the answers to the independent practice problems. Discuss any common errors or misconceptions. Briefly introduce the concept of supplementary angles as an extension of the lesson.

Interactive Exercises

  • Angle Puzzle
    Create a worksheet with various angle puzzles where students need to find missing angle measures using the principles learned in the lesson.

Discussion Questions

  • What does 'adjacent' mean in the context of angles?
  • How can you use the measure of the whole angle and one of its parts to find the measure of the other part?
  • Can you think of real-world examples where you might need to solve for an unknown angle?

Skills Developed

  • Problem-solving
  • Logical reasoning
  • Algebraic thinking
  • Geometric reasoning

Multiple Choice Questions

Question 1:

What are adjacent angles?

Correct Answer: Angles that share a vertex and a side

Question 2:

If angle ABC is 80 degrees and angle ABD is 30 degrees, what is the measure of angle DBC (assuming D lies between A and C)?

Correct Answer: 50 degrees

Question 3:

Angle XYZ and angle ZYA are adjacent angles. If angle XYZ is 65 degrees and angle XYA is 110 degrees, what is the measure of angle ZYA?

Correct Answer: 175 degrees

Question 4:

What operation would you use to find the missing angle measurement if you know the total angle measure and one adjacent angle's measure?

Correct Answer: Subtraction

Question 5:

Which of the following is an example of setting up an equation to solve for an unknown angle?

Correct Answer: x + 40 = 90

Question 6:

If angle LMN is 120 degrees and angle LMO is x degrees and angle OMN is 50 degrees, which equation can be used to find x?

Correct Answer: x + 50 = 120

Question 7:

Adjacent angles always share a:

Correct Answer: Side and vertex

Question 8:

What is the difference between acute and obtuse angles?

Correct Answer: Acute angles are smaller than 90 degrees, obtuse angles are larger than 90 degrees

Question 9:

If two angles form a straight line, what is their total measure?

Correct Answer: 180 degrees

Question 10:

In the problem, if the combined angle BOD is 70 degrees and the adjacent angle DOC is 45 degrees, what is the measure of angle COB?

Correct Answer: 25 degrees

Fill in the Blank Questions

Question 1:

Angles that share a common vertex and side are called ________ angles.

Correct Answer: adjacent

Question 2:

To find the measure of a missing adjacent angle, you need to ________ the known angle from the total angle measure.

Correct Answer: subtract

Question 3:

If angle PQR is 135 degrees and angle PQS is 85 degrees, then the measure of angle SQR is ________ degrees.

Correct Answer: 50

Question 4:

An ________ is a point where two sides of an angle meet.

Correct Answer: vertex

Question 5:

The measure of a right angle is ________ degrees.

Correct Answer: 90

Question 6:

If two angles combine to form a straight angle, they are called ________ angles.

Correct Answer: supplementary

Question 7:

In geometry, angles are measured in units called ________.

Correct Answer: degrees

Question 8:

A straight line forms an angle of ________ degrees.

Correct Answer: 180

Question 9:

The sum of two adjacent angles is equal to the measure of the ________ angle they form.

Correct Answer: combined

Question 10:

In the example from the video, the mystery angle COB was found by subtracting the known angle DOC from the total angle ________.

Correct Answer: BOD

Educational Standards

7.GM.3:Use mathematical models and reasoning with proportions and ratios to determine measurements, justify formulas, and solve problems. 7.A.3:Represent mathematical situations using equations and inequalities involving variables and rational numbers.

Teaching Materials

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