Math Problem Statement
Solution
To find the size of angle , we can use the properties of angles in triangles and around straight lines.
Step-by-step solution:
-
Angles on a straight line: The angle labeled and the adjacent angle (the exterior angle at the triangle's vertex) are supplementary, meaning their sum is because they form a straight line. Thus, the exterior angle is:
-
Sum of angles in a triangle: The interior angles of a triangle must sum to . The three angles in the triangle are:
- (given),
- (unknown), and
- the exterior angle we just found, which is .
Using the sum of interior angles:
-
Solve for : Simplifying the equation:
Thus, the size of angle is .
Would you like more details or have any questions? Here are five related questions for further understanding:
- How would the solution change if the exterior angle was different?
- Can you explain why the sum of angles in a triangle is always ?
- How would you find the exterior angle of a polygon with more than three sides?
- What are the properties of supplementary angles on a straight line?
- How can this method be applied to non-right triangles?
Tip: Always remember the sum of the angles in any triangle is , which is a key property used to solve for unknown angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles in Triangles
Supplementary Angles
Formulas
Sum of angles in a triangle = 180°
Supplementary angles on a straight line = 180°
Theorems
Sum of angles in a triangle
Supplementary Angles
Suitable Grade Level
Grades 6-8