Inscribed Angles in Quadrilaterals

The video tutorial covers solving for missing variables in inscribed quadrilaterals. Example A involves finding x, y, and z using properties of opposite angles and intercepted arcs. Example B uses algebraic expressions to solve for x and y. Example C demonstrates quick calculations for x and y in a circle. The tutorial emphasizes understanding the properties of inscribed quadrilaterals and applying algebraic techniques.

In an inscribed quadrilateral, if one angle is 80 degrees, what is the measure of its opposite angle?

• 80 degrees

• 100 degrees

• 90 degrees

• 180 degrees

If angle y is opposite to 71 degrees in an inscribed quadrilateral, what is the value of y?

• 109 degrees

• 89 degrees

• 71 degrees

• 180 degrees

What is the value of z if it is opposite to 93 degrees in an inscribed quadrilateral?

• 180 degrees

• 90 degrees

• 87 degrees

• 93 degrees

An inscribed angle intercepts arcs of 58 and 106 degrees. What is the measure of the angle?

• 82 degrees

• 164 degrees

• 58 degrees

• 106 degrees

In Example B, if 7x + 1 is opposite to 105 degrees, what is the value of x?

• 10.57

• 11

• 12

• 9.5

In Example B, what is the value of y if 4y + 14 and 7y + 1 are opposite angles?

• 16 degrees

• 14 degrees

• 15 degrees

• 13 degrees

In Example C, if x is opposite to 108 degrees, what is the value of x?

• 108 degrees

• 72 degrees

• 90 degrees

• 180 degrees

In Example C, what is the value of y if it is opposite to 88 degrees?

• 90 degrees

• 92 degrees

• 88 degrees

• 180 degrees