Question

In the given figure, 𝒚=$(3k+25{)}^{\circ }$ and 𝒙=$(4k–55{)}^{\circ }$.What must the value of 𝒌 be for the lines to be parallel?

Answer 1

As seen in the figure, x and y form a pair of co-interior angles. As a result, for the lines to be parallel, the sum of these angles must be 180°.


x + y = 180° [co-interior angles]
4k - 55° + 3k + 25° = 180°
7k = 180° +55° - 25° = 210°
k = 30°