Question

The four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4. The four angles of the quadrilateral are blank (30, 45, or 85) second blank (60, 75, or 90) third blank (115, 135, or 150) and fourth blank (105, 120, or 125).

A. 85, 75, 135, 105

B. 30, 60, 115, 120

C. 45, 90, 150, 125

D. 85, 60, 135, 120

Answer 1

The four angles of the inscribed quadrilateral are 85, 75, 135, and 105 degrees.

Step-by-step explanation:

The four angles of the quadrilateral are 85, 75, 135, and 105 degrees. The ratio of the angles of an inscribed quadrilateral is equal to the ratio of the lengths of the arcs they subtend.

Let's assume the ratio of the lengths of the arcs formed by the four vertices of the quadrilateral is 1:2:5:4. Since the sum of the angles in a circle is 360 degrees, we can calculate the size of each angle:

1. The first angle can be calculated as 1 / (1+2+5+4) * 360 = 85 degrees.
2. The second angle can be calculated as 2 / (1+2+5+4) * 360 = 75 degrees.
3. The third angle can be calculated as 5 / (1+2+5+4) * 360 = 135 degrees.
4. The fourth angle can be calculated as 4 / (1+2+5+4) * 360 = 105 degrees.

Therefore, the correct answer is A. 85, 75, 135, 105.