Question

Point P is the center of the circle in the figure above. What is the value of x?

Answer 1

Answer:

x = 80°

Step-by-step explanation:

To find x, we need to create an equation.

Recall that the sum of all the 4 interior angles of a quadrilateral = 360°.

Therefore:

m<B + m<A + m<C + m<P = 360°

m<B = 20° (given)

m<C = 20° (given)

m<A = ½*x = x/2 (inscribed angle theorem)

m<P = (360 - x)°

Plug in the values and solve for x

$20 + \frac{x}{2} + 20 + (360 - x) = 360$

$20 + \frac{x}{2} + 20 + 360 - x = 360$

Collect like terms

$20 + 20 + 360 + \frac{x}{2} - x = 360$

$400 + \frac{x}{2} - x = 360$

Subtract 400 from each side

$400 + \frac{x}{2} - x - 400 = 360 - 400$

$\frac{x}{2} - x = -40$

$\frac{x - 2x}{2} = -40$

$\frac{-x}{2} = -40$

Multiply both sides by 2

$\frac{-x}{2} \times 2 = -40 \times 2$

$-x = -80$

Divide both sides by -1

$\frac{-x}{-1} = \frac{-80}{-1}$

$x = 80$