Question

In IJKL, side IJ || side KL $\angle I={108}^{\circ }\angle K={53}^{\circ }$then find the measures of J and L.

Answer 1

In IJKL,
IL is the transversal.
$\angle I={108}^{\circ }\text{[Given]}$
$\angle I+\angle L={180}^{\circ }\text{[Interior angles on same side of transversal are supplementary]}$
${108}^{\circ }+\angle L={180}^{\circ }$
$\angle L=180-108={72}^{\circ }$
KJ is the transversal.
$\angle K={53}^{\circ }\text{[Given]}$
$\angle K+\angle J={180}^{\circ }\text{[Interior angles on same side of transversal are supplementary]}$
${53}^{\circ }+\angle J={180}^{\circ }$
$\angle J=180-53={127}^{\circ }$
Hence measure of $\angle J\text{and}\angle L\text{are}{127}^{\circ }and{72}^{\circ }\text{respectively.}$