Given:
The figure of a trapezium.
To find:
The measures of missing angle [tex]m\angle K, m\angle M[/tex].
Solution:
In the given figure [tex]JK\parallel ML[/tex].
If a transversal line intersect the two parallel lines, then the same sides interior angles are supplementary angles.
[tex]m\angle J+m\angle M=180^\circ[/tex] (Supplementary angles)
[tex]87^\circ+m\angle M=180^\circ[/tex]
[tex]m\angle M=180^\circ-87^\circ[/tex]
[tex]m\angle M=93^\circ[/tex]
Similarly,
[tex]m\angle L+m\angle K=180^\circ[/tex] (Supplementary angles)
[tex]51^\circ+m\angle K=180^\circ[/tex]
[tex]m\angle K=180^\circ-51^\circ[/tex]
[tex]m\angle K=129^\circ[/tex]
Therefore, [tex]m\angle M=93^\circ[/tex] and [tex]m\angle K=129^\circ[/tex].
