Atriangle has a square on its three sides as shown below. what is the value of x

using the pythagorean theorem

a^2+b^2 = c^2   where c is the hypotenuse

9^2 +12^2 = x^2

81 + 144 = x^2

225 = x^2

taking the square root of each side

sqrt(225) = x

15 =x

x = 15 inches

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

this answer is !