Math Problem Statement
Solution
Let's analyze each question in turn.
Question 3
In this problem:
- is the center of the circle.
- The segments .
- We are given , and we need to find .
Since , each of these segments subtends an equal angle at the center. This divides the entire angle around the center (360 degrees) into 4 equal parts.
-
Calculate Each Angle Subtended:
Since , , , and are equal, -
Find :
Since is less than 90 degrees, it implies that the question is to evaluate the sum of angles involved in the
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Math Problem Analysis
Mathematical Concepts
Geometry
Circles
Angles at the Center of a Circle
Inscribed Angles
Formulas
Angle subtended by equal arcs at the center
Relationship between inscribed and central angles
Theorems
Inscribed Angle Theorem
Central Angle Theorem
Suitable Grade Level
Grades 9-10
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