Math Problem Statement
Solution
The problem asks to determine the type of triangle and the sizes of the angles and , based on the provided diagram.
Step-by-Step Solution:
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Identify Known Angles:
- From the diagram, we know that the exterior angle at is .
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Use of Exterior Angle Theorem: The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is equal to the sum of and :
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Determine Third Angle: Since the sum of all angles in any triangle is , the angle at is given by:
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Solve for and : Now that we know the angle at , we can use it in the triangle . The sum of the interior angles of a triangle is also , so we have: Substituting the value into this equation: This equation confirms that our values are consistent.
Thus, the triangle is scalene (since all angles are different), and the angles are as follows:
Would you like further details on how to handle these types of geometry problems?
Related Questions:
- How can you calculate the length of the sides of this triangle if given?
- What is the exterior angle theorem in more detail?
- Can the type of triangle change if one of the angles is altered?
- How can you apply trigonometry to find the side lengths given angles and one side?
- How do we classify triangles based on their angles?
Tip: Always remember that the sum of the angles in any triangle must be , which is helpful for finding unknown angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangles
Angles
Formulas
Sum of interior angles of a triangle: α + β + γ = 180°
Exterior angle theorem: Exterior angle = sum of non-adjacent interior angles
Theorems
Exterior Angle Theorem
Suitable Grade Level
Grades 7-9
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