Solving Equations and Angles

The video tutorial explains the property of inscribed quadrilaterals in a circle, focusing on how opposite angles are supplementary, meaning they add up to 180 degrees. The instructor demonstrates solving an algebraic equation to find specific angles in a quadrilateral, emphasizing the concept of supplementary angles. The video concludes with a recap of the key points discussed.

What does it mean for a quadrilateral to be inscribed in a circle?

• It is a regular polygon.

• It has a right angle.

• All its vertices lie on the circumference of the circle.

• All its sides are equal.

What is the property of opposite angles in an inscribed quadrilateral?

• They are equal.

• They are complementary.

• They are supplementary.

• They are congruent.

What does it mean for two angles to be supplementary?

• They add up to 180 degrees.

• They are equal.

• They are adjacent.

• They add up to 90 degrees.

How do you set up an equation to solve for unknown angles in an inscribed quadrilateral?

• By multiplying the angles.

• By equating the angles to 90 degrees.

• By adding the angles and setting them equal to 180 degrees.

• By subtracting the angles from 360 degrees.

What is the first step in solving the equation 3x + 4 + x + 2 = 180?

• Multiply both sides by 3.

• Subtract 4 from both sides.

• Combine like terms.

• Divide both sides by 2.

After combining like terms, what is the equation to solve for x?

• 4x = 180

• 3x + 6 = 180

• x + 6 = 180

• 4x + 6 = 180

What is the value of x when you solve the equation 4x = 174?

• 44

• 45

• 43.5

• 42.5

What is the measure of the angle represented by x + 2 when x = 43.5?

• 43 degrees

• 45.5 degrees

• 46 degrees

• 44.5 degrees

What is the measure of the angle represented by 3x + 4 when x = 43.5?

• 136 degrees

• 132 degrees

• 134.5 degrees

• 130 degrees

What should the sum of the opposite angles in an inscribed quadrilateral be?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees