At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To solve the problem of finding the four angles of an inscribed quadrilateral where the vertices divide the circle in the ratio [tex]\(1: 2: 5: 4\)[/tex], let’s proceed step by step:
1. Understanding the Ratio and Total Parts: First, let's recognize that the circle is divided into parts by the vertices in the ratio [tex]\(1:2:5:4\)[/tex]. Adding these parts together, we get:
[tex]\[ 1 + 2 + 5 + 4 = 12 \][/tex]
So, the circle's circumference is divided into 12 equal parts.
2. Finding Individual Angles: The sum of a circle's angles is [tex]\(360^\circ\)[/tex]. We can determine each angle corresponding to each part by multiplying the ratio by [tex]\(\frac{360^\circ}{12}\)[/tex].
- First Part ([tex]\(1\)[/tex] part out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{1}{12} \right) \times 360^\circ = 30.0^\circ \][/tex]
- Second Part ([tex]\(2\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{2}{12} \right) \times 360^\circ = 60.0^\circ \][/tex]
- Third Part ([tex]\(5\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{5}{12} \right) \times 360^\circ = 150.0^\circ \][/tex]
- Fourth Part ([tex]\(4\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{4}{12} \right) \times 360^\circ = 120.0^\circ \][/tex]
3. Assigning the Angles: Now we have determined the angles, which are [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
Thus, the four angles of the quadrilateral are [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
To fill in the drop-down menus correctly, select:
- The first menu: [tex]\(30.0\)[/tex]
- The second menu: [tex]\(,\)[/tex]
- The third menu: [tex]\(60.0\)[/tex]
- The fourth menu: [tex]\(,\)[/tex]
- The fifth menu: [tex]\(150.0\)[/tex]
- The sixth menu: [tex]\(\text{}^\circ\)[/tex]
- The seventh menu: [tex]\(120.0\)[/tex]
So, the answer is: [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
1. Understanding the Ratio and Total Parts: First, let's recognize that the circle is divided into parts by the vertices in the ratio [tex]\(1:2:5:4\)[/tex]. Adding these parts together, we get:
[tex]\[ 1 + 2 + 5 + 4 = 12 \][/tex]
So, the circle's circumference is divided into 12 equal parts.
2. Finding Individual Angles: The sum of a circle's angles is [tex]\(360^\circ\)[/tex]. We can determine each angle corresponding to each part by multiplying the ratio by [tex]\(\frac{360^\circ}{12}\)[/tex].
- First Part ([tex]\(1\)[/tex] part out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{1}{12} \right) \times 360^\circ = 30.0^\circ \][/tex]
- Second Part ([tex]\(2\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{2}{12} \right) \times 360^\circ = 60.0^\circ \][/tex]
- Third Part ([tex]\(5\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{5}{12} \right) \times 360^\circ = 150.0^\circ \][/tex]
- Fourth Part ([tex]\(4\)[/tex] parts out of [tex]\(12\)[/tex]):
[tex]\[ \left(\frac{4}{12} \right) \times 360^\circ = 120.0^\circ \][/tex]
3. Assigning the Angles: Now we have determined the angles, which are [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
Thus, the four angles of the quadrilateral are [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
To fill in the drop-down menus correctly, select:
- The first menu: [tex]\(30.0\)[/tex]
- The second menu: [tex]\(,\)[/tex]
- The third menu: [tex]\(60.0\)[/tex]
- The fourth menu: [tex]\(,\)[/tex]
- The fifth menu: [tex]\(150.0\)[/tex]
- The sixth menu: [tex]\(\text{}^\circ\)[/tex]
- The seventh menu: [tex]\(120.0\)[/tex]
So, the answer is: [tex]\(30.0^\circ\)[/tex], [tex]\(60.0^\circ\)[/tex], [tex]\(150.0^\circ\)[/tex], and [tex]\(120.0^\circ\)[/tex].
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
