Question

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

Answer 1

The quadrilateral is cyclic, because the angle that the tangent and the radius meet forms a right angle. Since the two opposite angles are 90° each, they form a 180° summation. Thus, the four points are cyclic.

Now, the smaller ∠O is 135, which means x is 180 - 135 because the four points are concyclic. Thus ∠O + x = 180°
Hence, x = 180 - 135 = 45°

∴ x = 45°

Answer 2

For the inscribed angles quiz the answers are:

1: d(44)

2: a(74)

3: a(13,464 miles)

4: d(3.5 ft)

5: b(9.2)

6: d(56 degrees)

7: c(69.5 degrees)

8: d(84)

I just just took the quiz. So like it’s right.