Math Problem Statement
Solution
To solve this problem, we analyze the given information about triangle :
Given:
- (so the triangle is isosceles).
- .
- We need to find (labeled ).
Step-by-step Solution:
-
Sum of angles in a triangle: The sum of the internal angles in any triangle is always . Therefore:
-
Isosceles Triangle Property: Since , the angles opposite these equal sides are also equal. Thus:
-
Substitute known values: Replace and simplify:
Combine like terms:
-
Solve for : Subtract from both sides:
Divide by 2:
Final Answer:
The measure of is:
This corresponds to option B.
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Related Questions:
- What are the properties of isosceles triangles?
- How do you calculate the angles of a triangle given one angle?
- What is the sum of the interior angles of a polygon?
- How do you solve for missing angles in triangles with congruent sides?
- Can you explain exterior angles of triangles and their relationships?
Tip: Always use triangle symmetry to simplify calculations in isosceles and equilateral triangles!
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Math Problem Analysis
Mathematical Concepts
Triangle Angle Sum
Isosceles Triangle Properties
Basic Algebra
Formulas
Sum of angles in a triangle: ∠P + ∠Q + ∠R = 180°
Theorems
Isosceles Triangle Theorem
Suitable Grade Level
Grades 8-10
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