Sure, let's solve this problem step by step!
1. Understanding the Question:
- We are given the angles [tex]\(135^\circ\)[/tex], [tex]\(160^\circ\)[/tex], and [tex]\(50^\circ\)[/tex].
- We need to find the unknown angle [tex]\(x\)[/tex], knowing that the sum of these angles should equal [tex]\(360^\circ\)[/tex].
2. Setting Up the Equation:
- The sum of the given angles and the unknown angle [tex]\(x\)[/tex] should be [tex]\(360^\circ\)[/tex]. This can be written as:
[tex]\[
135^\circ + 160^\circ + 50^\circ + x = 360^\circ
\][/tex]
3. Summing the Known Angles:
- First, add the known angles:
[tex]\[
135^\circ + 160^\circ + 50^\circ = 345^\circ
\][/tex]
4. Solving for the Unknown Angle [tex]\(x\)[/tex]:
- Substitute the sum of the known angles into the equation:
[tex]\[
345^\circ + x = 360^\circ
\][/tex]
- To isolate [tex]\(x\)[/tex], subtract [tex]\(345^\circ\)[/tex] from both sides of the equation:
[tex]\[
x = 360^\circ - 345^\circ
\][/tex]
- Perform the subtraction:
[tex]\[
x = 15^\circ
\][/tex]
5. Conclusion:
- The unknown angle [tex]\(x\)[/tex] is [tex]\(15^\circ\)[/tex].
- Hence, the angles sum up correctly to [tex]\(360^\circ\)[/tex].
To summarize, given the angles [tex]\(135^\circ, 160^\circ,\)[/tex] and [tex]\(50^\circ,\)[/tex] the unknown angle is [tex]\(15^\circ\)[/tex].
