[tex]\huge {\boxed{\tt{Solution :}}}[/tex]
Tell whether the angles are adjacent or vertical.
[tex]\sf { 1.) \: Adjacent} \\ \sf { 2.) \: Vertical } \\ \sf { 3.) \:Adjacent}[/tex]
Find the value of x.
4.)
[tex] \sf{{x}^ {\circ} = {110} ^ {\circ} \: [ \because {Vertically \: oppsite \: angles \: are \: equal.}]}[/tex]
5.)
[tex]\sf{ : \implies {x}^ {\circ} + {151} ^ {\circ} ={180} ^ {\circ} \: [\because{Sum\:of \: Adjacent\:angles \: is \: {180} ^ {\circ}.}] } \\ \\ \sf{ : \implies {x}^ {\circ} ={(180 - 151)}^ {\circ}} \\ \\ : \implies {\boxed{\tt{ {x}^ {\circ} ={29}^ {\circ}}}} [/tex]
6.)
[tex]\sf{ : \implies {x}^ {\circ} + {30} ^ {\circ} ={90} ^ {\circ} \: [ \because {Right\:angle \: is \: {90} ^ {\circ}.}] } \\ \\ \sf{ : \implies {x}^ {\circ} ={(90 - 30)}^ {\circ}} \\ \\ : \implies {\boxed{\tt{ {x}^ {\circ} ={60}^ {\circ}}}}[/tex]
7.)
[tex]\sf{ : \implies {x}^ {\circ} + {20} ^ {\circ} ={180} ^ {\circ} \: [\because{Sum\:of \: Adjacent\:angles \: is \: {180} ^ {\circ}.}] } \\ \\ \sf{ : \implies {x}^ {\circ} ={(180 - 20)}^ {\circ}} \\ \\ : \implies {\boxed{\tt{ {x}^ {\circ} ={160}^ {\circ}}}}[/tex]
8.)
[tex]\sf{ : \implies {x}^ {\circ} + {45} ^ {\circ} ={180} ^ {\circ} \: [\because{Sum\:of \: Adjacent\:angles \: is \: {180} ^ {\circ}.}] } \\ \\ \sf{ : \implies {x}^ {\circ} ={(180 - 45)}^ {\circ}} \\ \\ : \implies {\boxed{\tt{{x}^ {\circ} ={135}^ {\circ}}}}[/tex]
[tex]\rule {307}{2}[/tex]
