Answer: [tex]83^{\circ}[/tex]
Step-by-step explanation:
Given : Three of the six angles formed by the intersecting lines are labeled. Every other angle is labeled. Going clockwise, they are labeled 56 degrees, x, and 41 degrees.
From the given information , the suitable diagram is given below:
Since we know that , when two lines intersect , the vertical angles are equal.
Also, the combined angle of a point is 360°.
[It includes a pair of each of three angles ]
Thus, we have
[tex]2(56^{\circ})+2(x^{\circ})+2(41^{\circ})=360^{\circ}\\\\\Rightarrow\ 112^{\circ}+2x^{\circ}+82^{\circ}=360^{\circ}\\\\\Rightarrow\ 2x^{\circ}=360^{\circ}-194^{\circ}\\\\\Rightarrow\ 2x^{\circ}=166^{\circ}\\\\\Rightarrow\ x^{\circ}=\dfrac{166^{\circ}}{2}=83^{\circ}[/tex]
Hence, the measure of angle x =[tex]83^{\circ}[/tex]
