question_answer

 

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,      \[\angle x=115{}^\circ ,\text{ }\angle y=140{}^\circ \text{ }and\angle z=40{}^\circ \]