To determine the four angles of the quadrilateral inscribed in a circle, given that they divide the circle in the ratio [tex]\(1: 2: 5: 4\)[/tex], we need to follow these steps:
1. Understand the ratio: The circle is divided into parts with a ratio of 1:2:5:4.
2. Sum of the parts: The total of these parts is [tex]\(1 + 2 + 5 + 4 = 12\)[/tex].
3. Convert ratios to angles: The angles of the quadrilateral will be proportional to these parts, and since the total angle around a point (full circle) is [tex]\(360^\circ\)[/tex], we distribute [tex]\(360^\circ\)[/tex] according to the given ratio.
4. Calculate each angle:
- The part with the ratio [tex]\(1\)[/tex]: [tex]\(\frac{1}{12} \times 360^\circ = 30^\circ\)[/tex]
- The part with the ratio [tex]\(2\)[/tex]: [tex]\(\frac{2}{12} \times 360^\circ = 60^\circ\)[/tex]
- The part with the ratio [tex]\(5\)[/tex]: [tex]\(\frac{5}{12} \times 360^\circ = 150^\circ\)[/tex]
- The part with the ratio [tex]\(4\)[/tex]: [tex]\(\frac{4}{12} \times 360^\circ = 120^\circ\)[/tex]
So, the four angles of the quadrilateral are [tex]\(30^\circ\)[/tex], [tex]\(60^\circ\)[/tex], [tex]\(150^\circ\)[/tex], and [tex]\(120^\circ\)[/tex].
Now, we can select the correct answer from each drop-down menu:
The four angles of the quadrilateral are
[tex]\[30 \text{ degrees}, 60 \text{ degrees}, 150 \text{ degrees} \text{, and } 120 \text{ degrees}\][/tex]
