Question

A quadrilateral ABCD is inscribed in a circle. Its diagonals inter-sectat. If AB 100°, BC 50and AD = BD, find mDXC.

a) 60°
b) 70°
c) 80°
d) 90°

Answer 1

In a quadrilateral ABCD inscribed in a circle, angle DXC is 100 degrees.

Step-by-step explanation:

In a quadrilateral ABCD inscribed in a circle, the opposite angles are supplementary. So, angle ADC is equal to 180 - angle ABC = 180 - 100 = 80 degrees.

Since AD = BD, angle CAD = angle CBD = 80/2 = 40 degrees.

Now, in triangle DXC, angle DXC + angle DCA + angle DCX = 180 degrees.

Since angle DCA = angle DCX = 40 degrees, we can substitute these values:

angle DXC + 40 + 40 = 180 degrees.

From this equation:

angle DXC = 180 - 40 - 40 = 100 degrees.

So, the answer is d) 90 degrees.