Math Problem Statement
Solution
The image shows a pentagon with various angles marked, and the goal is likely to solve for the unknown angles based on the given information.
Information from the image:
- One of the internal angles is .
- Another internal angle is .
- The angle adjacent to the exterior angle is labeled as .
- There is an internal angle labeled .
- The angle adjacent to and forming a straight line is .
We can solve for the unknown angle by using the following facts:
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Sum of interior angles of a pentagon: The sum of the interior angles of any pentagon is given by the formula: where is the number of sides. For a pentagon, , so:
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Straight-line angles: The angle adjacent to and is part of a straight line, so they should sum to :
Now that we have , we can calculate the remaining angles and verify the sum of the interior angles.
- The angle marked is .
- The remaining angle is already given as .
Now let's check the sum of all the angles:
Thus, everything checks out.
Final Answer:
- .
Would you like further details or clarification on any part of this solution?
Here are five related questions you might explore:
- How do we calculate the sum of the interior angles of any polygon?
- What is the relationship between exterior and interior angles in polygons?
- How can we determine angles when they form a straight line?
- How do we use algebraic expressions in geometry to find unknown angles?
- How can the knowledge of basic angle properties be applied to more complex polygons?
Tip: Always remember that adjacent angles on a straight line sum up to .
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Math Problem Analysis
Mathematical Concepts
Geometry
Polygons
Interior Angles
Exterior Angles
Linear Pair of Angles
Formulas
Sum of Interior Angles of a Polygon: (n - 2) * 180°
Linear Pair of Angles: Sum of two adjacent angles on a straight line equals 180°
Theorems
Sum of Interior Angles Theorem
Linear Pair Theorem
Suitable Grade Level
Grades 8-10