Find the values of the angles x, y and z in each of the following: |
(a) |
(b) |
Answer:
(a) \[\angle x=55{}^\circ \] [vertically opposite angles] \[\angle y+55{}^\circ =180{}^\circ \] [linear pair] \[\angle y\text{ }=180{}^\circ -55{}^\circ -125{}^\circ \] \[\angle z=\angle y=125{}^\circ \] [vertically opposite angles] Hence,\[\angle x=55,\text{ }\angle y=125{}^\circ \text{ }and\angle z=125{}^\circ \] (b) \[\angle y+40{}^\circ =180\] [by linear pair] \[\angle y+40{}^\circ =180{}^\circ -40{}^\circ \] \[\angle y=140{}^\circ \] \[\angle z=40{}^\circ \] [vertically opposite angles] \[\therefore \,\,\angle x+25{}^\circ +\angle z=180{}^\circ \] [by linear pair] \[\therefore \,\,\angle x+25{}^\circ +40{}^\circ =180{}^\circ \] \[\angle x=180{}^\circ -65{}^\circ =115{}^\circ \] Hence, \[\angle x=115{}^\circ ,\text{ }\angle y=140{}^\circ \text{ }and\angle z=40{}^\circ \]
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