Answer:
Diagram a:
[tex]{ \rm{x + 2x = 180 - (81)}} \\ { \rm{3x = 99}} \\ { \underline{ \underline{ \rm{ \: \: x = 33 \: \: }}}} \\ [/tex]
Diagram b:
[tex]{ \rm{64 + 90 = (x + 8)}} \\ { \rm{154 = x + 8}} \\ { \underline{ \underline{ \rm{ \: \: x = 146 \: \: }}}}[/tex]
Diagram c:
[tex]{ \rm{(2x + 4) + (180 - 132) + (180 - 112) = 180}} \\ { \rm{(2x + 4) + 48 + 68 = 180}} \\ { \rm{2x + 118 = 180}} \\ { \rm{2x = 62}} \\ { \underline{ \underline{ \rm{ \: \: x = 31 \: \: }}}}[/tex]
Diagram d:
[tex]{ \rm{(3x + 2) + (2x + 18) = 90 }}\\ { \rm{5x + 20 = 90}} \\ { \rm{5x = 70}} \\ { \underline{ \underline{ \rm{ \: \: x = 14 \: \: }}}}[/tex]
Note: The rule used is "The sum of two interior angles of a triangle are equal to the value of the exterior angle"
