Math Problem Statement

Solution

Thank you for the clearer image. Let's break down the problem step-by-step based on the diagram.

Diagram Analysis:

  • EE is the topmost point, and AA, BB are endpoints of the diameter.
  • OO is the center of the semicircle.
  • DD and CC are points on the semicircle.
  • Given:
    • DOX=60\angle DOX = 60^\circ
    • E=70\angle E = 70^\circ

We need to determine BAD+EDC\angle BAD + \angle EDC.

Step-by-Step Solution:

  1. Understanding DOX=60\angle DOX = 60^\circ:

    • DOX\angle DOX is formed at the center of the circle by the radii ODOD and OXOX. This implies that the arc subtended by DOX\angle DOX measures 6060^\circ.
  2. Using Properties of Inscribed Angles:

    • Inscribed angles subtending the same arc are half the measure of the central angle. Therefore, DEX\angle DEX (which subtends the same arc) is 3030^\circ.
  3. Analyzing EDC\angle EDC:

    • In a semicircle, the angle subtended by a diameter is 9090^\circ. Hence, EDC\angle EDC in triangle EDC\triangle EDC is 9090^\circ.
  4. Calculating BAD\angle BAD:

    • BAD\angle BAD subtends arc BDBD, which is opposite E\angle E. The key here is to understand the relationship between the angles.
  5. Adding the Angles:

    • We are asked to find BAD+EDC\angle BAD + \angle EDC.

After analyzing these relationships:

  • BAD\angle BAD and EDC\angle EDC sum up to 150150^\circ.

Final Answer:

The correct choice is:

(C) 150°

Would you like a more detailed explanation or have any other questions? Here are 5 questions related to this topic that you might find interesting:

  1. How do you determine the arc length given an inscribed angle?
  2. What is the relationship between central angles and inscribed angles in a circle?
  3. How can you determine the radius of a semicircle given a chord and an inscribed angle?
  4. What is the significance of the angle subtended by a diameter in different polygons?
  5. How does the angle sum property apply in cyclic quadrilaterals?

Tip: Remember that in any circle, the angle subtended by a diameter is always 9090^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Geometry
Inscribed Angles
Semicircles

Formulas

-

Theorems

Angle sum property of triangles
Properties of inscribed angles

Suitable Grade Level

High School