To find the measures of the angles in a quadrilateral given the ratio [tex]\(3:5:4:6\)[/tex], we need to follow these steps:
1. Understand the properties of a quadrilateral: The sum of all interior angles in a quadrilateral is [tex]\(360\)[/tex] degrees.
2. Identify the ratio of the angles: The ratio given for the angles is [tex]\(3:5:4:6\)[/tex].
3. Calculate the total parts of the ratio: Add up the parts of the ratio to find the total sum of the ratio components.
[tex]\[
3 + 5 + 4 + 6 = 18
\][/tex]
4. Determine the value of one part of the ratio: Since the angles together sum to [tex]\(360\)[/tex] degrees, each part of the ratio represents a fraction of [tex]\(360\)[/tex] degrees.
[tex]\[
\text{One part} = \frac{360}{18} = 20 \text{ degrees}
\][/tex]
5. Calculate the measure of each angle using the ratio:
- The first angle corresponds to [tex]\(3\)[/tex] parts:
[tex]\[
3 \times 20 = 60 \text{ degrees}
\][/tex]
- The second angle corresponds to [tex]\(5\)[/tex] parts:
[tex]\[
5 \times 20 = 100 \text{ degrees}
\][/tex]
- The third angle corresponds to [tex]\(4\)[/tex] parts:
[tex]\[
4 \times 20 = 80 \text{ degrees}
\][/tex]
- The fourth angle corresponds to [tex]\(6\)[/tex] parts:
[tex]\[
6 \times 20 = 120 \text{ degrees}
\][/tex]
By following these steps, we find that the measures of the angles in the quadrilateral are:
[tex]\[
60 \text{ degrees}, 100 \text{ degrees}, 80 \text{ degrees}, 120 \text{ degrees}
\][/tex]
