Question 11 (Essay Worth 10 points)
(09.02 MC)
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle P? You must show all work and calculations to receive credit
R(3y+8)
O(2x)
Q(2x+4)
P y



Answer :

Answer:

To solve this problem, we need to use the properties of inscribed quadrilaterals and the relationships between the angles and sides of a circle.

Given information:

- Quadrilateral OPQR is inscribed inside a circle.

Step 1: Identify the properties of an inscribed quadrilateral.

In an inscribed quadrilateral, the opposite angles are supplementary, meaning their sum is 180 degrees.

Step 2: Set up an equation to find the measure of angle P.

Let the measure of angle P be y.

Since the opposite angles of the inscribed quadrilateral are supplementary, we can write:

y + (3y + 8) = 180 degrees

Step 3: Solve the equation for y.

y + (3y + 8) = 180

4y + 8 = 180

4y = 172

y = 43 degrees

Therefore, the measure of angle P is 43 degrees.

Step-by-step explanation:

I hope it helps hehehe