Solving inscribed quadrilaterals | Mathematics II | High School Math | Khan Academy

TL;DR

In this video, the measure of angle D in an inscribed quadrilateral is found using the relationship between inscribed angles and the arcs they intercept.

Transcript

• [Voiceover] What I wanna do in this video is see if we can find the measure of angle D, if we could find the measure of angle D and like always, pause this video, and see if you can figure it out. And I'll give you a little bit of a hint. It'll involve thinking about how an inscribed angle relates to the corresponding to the measure of the arc th... Read More

Key Insights

• 🔺 Inscribed angles are related to the arcs they intercept, with the measure of an inscribed angle being half the measure of the intercepted arc.
• 🫠 The measure of the arc that completes the circle can be used to determine the measure of other arcs in the same circle.
• 🫠 The sum of the measures of arcs in a circle is 360 degrees.

Questions & Answers

Q: How can the measure of angle D be found?

The measure of angle D can be found by determining the measure of the arc it intercepts, which is half of that value.

Q: How is the measure of the arc that completes the circle known?

The measure of the arc is known because the video mentions that the inscribed angle intercepting it is 45 degrees.

Q: What is the relationship between the measures of arc LIW, WL, and the large purple arc?

The sum of the measures of arc LIW and WL, along with the purple arc, equal 360 degrees.

Q: Are the opposite angles of an inscribed quadrilateral always supplementary?

The video hints at this possibility, but further investigation and proof are needed to determine if opposite angles of an inscribed quadrilateral always add up to 180 degrees.

Summary & Key Takeaways

• Angle D intercepts a large arc in the shape of a purple color.

• The measure of an inscribed angle is half the measure of the arc it intercepts.

• By knowing the measure of the arc that completes the circle, the measure of angle D can be determined.