Math Problem Statement
Solution
To solve this problem, we need to analyze the geometry of the circumscribed angle.
The problem shows a circumscribed angle formed by the tangents to a circle, with the angle's measure given as , and one of the intercepted arcs labeled as .
Key Concept:
In a circle, the measure of a circumscribed angle (an angle formed outside the circle by two tangents) is half the difference between the measures of the intercepted arcs.
Given:
- The circumscribed angle is .
- One of the arcs intercepted by the angle is labeled (degrees).
Let's denote:
- The measure of the other arc as (which is the arc opposite to ).
Since the angle is formed by tangents, the total measure of both arcs should add up to because the entire circle's arc measures sum to .
Thus, we have: So,
Applying the Circumscribed Angle Formula:
The measure of the circumscribed angle is:
Substitute : Multiply both sides by 2: Add 350 to both sides: Divide by 4:
However, this does not match any of the answer choices, indicating there might be a mistake in setup.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circumscribed Angle
Circle Properties
Formulas
Circumscribed angle = (1/2) * (larger intercepted arc - smaller intercepted arc)
Theorems
Circumscribed Angle Theorem
Suitable Grade Level
Grades 9-10