question_answer

            In figure, find the measures of \[\angle \]PON and \[\angle \]NPO.

Answer:

In \[\Delta LOM,\text{ }\angle OLM+\angle OML+\angle LOM=180{}^\circ \] \[70{}^\circ +20{}^\circ +\angle LOM=180{}^\circ \] \[90{}^\circ +\angle LOM=180{}^\circ \] \[\angle LOM=180{}^\circ -90{}^\circ =90{}^\circ \] \[\angle LOM=\angle PON\]                                                                                                                                 [since, vertically opposite angles are equal] \[\angle PON=90{}^\circ \] In\[\Delta PON\], \[\angle PON-\angle NPO+\angle ONP=180{}^\circ \] \[90{}^\circ +\angle NPO+70{}^\circ =180{}^\circ \] \[\angle NPO=180{}^\circ -160{}^\circ =20{}^\circ \]