Math Problem Statement
Find the sizes of the three unknown angles in the image above
Solution
To find the sizes of the unknown angles , , and in the image, we will use the properties of vertically opposite angles and the fact that angles on a straight line sum to .
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Identifying vertically opposite angles:
- The angle labeled is vertically opposite to angle .
- Vertically opposite angles are equal, so:
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Using the fact that angles on a straight line sum to :
- Angle and the angle form a linear pair. Therefore:
- Solving for :
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Using the fact that angles around a point sum to :
- The angles , , and are formed around a point. Therefore:
- We already know and . Substituting these values:
- Solving for :
So, the sizes of the unknown angles are:
Would you like more details or have any questions? Here are 5 additional questions you might find interesting:
- How do you find the value of an unknown angle in a right triangle?
- What is the relationship between corresponding angles and parallel lines?
- How can you use the exterior angle theorem to solve problems?
- What are the properties of supplementary and complementary angles?
- How do you determine the angles in an equilateral triangle?
Tip: Always look for known angle relationships, such as vertically opposite angles and angles on a straight line, to simplify the process of finding unknown angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles
Properties of Angles
Formulas
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Theorems
Vertically Opposite Angles Theorem
Angles on a Straight Line Theorem
Angles around a Point Theorem
Suitable Grade Level
Grades 7-9
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