2 Inscribed Angle Geometry Problems

In summary, the conversation discusses finding x for problem (1) and x and y for problem (2) using properties of inscribed quadrilaterals and angles. The individual is unsure how to directly input images into the thread and asks for help. The conversation also mentions the possibility of using theorems relating angles to arcs and inscribed quadrilaterals. The first step for problem 1 is suggested to be constructing an inscribed quadrilateral and relating the angle opposite of Y to the arc segment XYW. For problem 2, it is mentioned that opposite angles are related in some way.
  • #1
DEMJR
14
0
I want to find x for (1) and x and y for (2). I am not sure how to put the images directly into the thread so I apologize if you do not like having to click on them.

On the first one, I do not know how we can find this without knowing that XW is a diameter (it is not given as one in the problem).

On the second one I am guessing I must use some type of property of quadrilaterals?

Any help will be greatly appreciated.
 

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  • #2
You posted the images properly!

Are there any theorems in your book relating angles to arcs (for the first problem) or angles and inscribed quadrilaterals (for the second problem)?

Your first step for problem 1 should be to construct an inscribed quadrilateral. The angle opposite of Y can be related to the arc segment XYW.

For the second problem, opposite angles are related to each other in some fashion.
 

Related to 2 Inscribed Angle Geometry Problems

1. What is an inscribed angle in geometry?

An inscribed angle is an angle formed by two chords of a circle that have a common endpoint, called the vertex, on the circle and the other two endpoints on the circle.

2. How do you find the measure of an inscribed angle?

The measure of an inscribed angle is half the measure of its intercepted arc. You can use the central angle theorem, which states that the central angle is twice the inscribed angle, to find the measure of an inscribed angle.

3. What is the relationship between an inscribed angle and its intercepted arc?

The intercepted arc of an inscribed angle is the part of the circle intercepted by the angle. The measure of the intercepted arc is twice the measure of the inscribed angle.

4. How do you solve inscribed angle geometry problems?

To solve inscribed angle geometry problems, you can use the properties of inscribed angles and their intercepted arcs. You can also use theorems such as the inscribed angle theorem and the central angle theorem.

5. What real-world applications use inscribed angles?

Inscribed angles are used in various real-world applications such as architecture, engineering, and navigation. For example, they are used in the design of circular structures such as bridges and roundabouts, and in navigation to determine the direction of a ship or plane based on the angle between two landmarks.

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