To find the missing angle in a quadrilateral when given the other three angles, we can use the fact that the sum of all interior angles in a quadrilateral is always [tex]\(360^{\circ}\)[/tex].
Here are the steps to solve the problem:
1. Identify the given angles:
- The first angle is [tex]\(580^{\circ}\)[/tex].
- The second angle is [tex]\(170^{\circ}\)[/tex].
- The third angle is [tex]\(122^{\circ}\)[/tex].
2. Sum the given angles:
- Add the three given angles: [tex]\(580^{\circ} + 170^{\circ} + 122^{\circ}\)[/tex].
This results in a sum of:
[tex]\[
580^{\circ} + 170^{\circ} + 122^{\circ} = 872^{\circ}
\][/tex]
3. Determine the total sum of angles in a quadrilateral:
- The sum of interior angles in any quadrilateral is always [tex]\(360^{\circ}\)[/tex].
4. Calculate the unknown angle:
- Subtract the sum of the given angles from the total sum of angles in a quadrilateral to find the missing angle:
[tex]\[
\text{Unknown angle} = 360^{\circ} - 872^{\circ} = -512^{\circ}
\][/tex]
The result indicates that the missing angle is [tex]\(-512^{\circ}\)[/tex], which is just a way of saying that the given angles already exceed the total sum of [tex]\(360^{\circ}\)[/tex] for a quadrilateral. In practical terms, having such angles would imply something incorrect in the given values, as angles in a typical quadrilateral should sum up to exactly [tex]\(360^{\circ}\)[/tex].
