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
[tex] 20 + \frac{x}{2} + 20 + (360 - x) = 360 [/tex]
[tex] 20 + \frac{x}{2} + 20 + 360 - x = 360 [/tex]
Collect like terms
[tex] 20 + 20 + 360 + \frac{x}{2} - x = 360 [/tex]
[tex] 400 + \frac{x}{2} - x = 360 [/tex]
Subtract 400 from each side
[tex] 400 + \frac{x}{2} - x - 400 = 360 - 400 [/tex]
[tex] \frac{x}{2} - x = -40 [/tex]
[tex] \frac{x - 2x}{2} = -40 [/tex]
[tex] \frac{-x}{2} = -40 [/tex]
Multiply both sides by 2
[tex] \frac{-x}{2} \times 2 = -40 \times 2 [/tex]
[tex] -x = -80 [/tex]
Divide both sides by -1
[tex] \frac{-x}{-1} = \frac{-80}{-1} [/tex]
[tex] x = 80 [/tex]
