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Answer 1

Step-by-step explanation:

angles are not clear that which we have to find

follow me pleass

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ : \star : \sf{ \red{Linear \: \: pair \: \: of \: \: angles \: \: must \: \: add \: \: up \: \: }} \\ \: \: \: \: \: \: \: \: \sf{ \red{to \: \: 180 \degree}.}$

$\underline{ \text{ \: In \: the \: figure, \: }} \\ \\ \: \: \: \: \: \: \: \: \tt{ \blue{\angle BAD + x = 180 \degree}} \\ \\ \tt {\blue {\implies 120 \degree + x = 180 \degree}} \\ \\ \tt{ \blue{ \implies x = 180 \degree - 120 \degree }} \\ \\ \: \: \: \tt{ \blue{ \therefore \: \: \: \: \: \: \: \: \underline{ \: \: x = 60 \degree\: }}}$

$\: \: \: \: \: \: \: \: \tt{ \green{\angle ABC + y = 180 \degree}} \\ \\ \tt{ \green{ \implies 80 \degree + y = 180 \degree}} \\ \\ \tt{ \green{\implies y = 180 \degree - 80 \degree}} \\ \\ \: \: \: \: \: \: \: \tt{ \green{ \therefore \: \: \: \underline{ \: \: \: y = 100 \degree \: }}}$

$\: \: \: \: \: \: \: \: \tt{ \pink{\angle BCD + z = 180 \degree}} \\ \\ \tt{ \pink{ \implies 60 \degree + z = 180 \degree}} \\ \\ \tt{ \pink{\implies z = 180 \degree - 60 \degree }} \\ \\ \: \: \: \: \: \: \: \: \tt{ \pink{ \therefore \: \: \underline{ \: \: \: z = 120 \degree \: }}}$

$\mathfrak{Again,} \\ \: \: \: \: \: \: \: \underline{ \mathfrak{ \: We \: \: know \: \: that, \: }} \\ \\ : \star : \sf{ \red{Sum \: \: of \: \: the \: \: four \: \: angles \: \: of \: \: a \: \: quadrilateral \: \: }} \\ \: \: \: \: \: \: \: \: \: \: \sf{ \red{is \: \: equal \: \: to \: \: 360 \degree}.}$

$\underline{ \text{ \: In \: the \: diagram, \: }} \\ \\ \: \: \: \: \sf{ 120 \degree + 80 \degree + 60 \degree + \angle CDA = 360 \degree} \\ \\ \sf{\implies 260 \degree + \angle CDA = 360 \degree} \\ \\ \sf{ \implies \angle CDA = 360 \degree - 260 \degree } \\ \\ \: \: \: \: \: \: \: \: \: \sf{ \therefore \: \underline{ \: \angle CDA = 100 \degree\: }}$

$\underline{ \mathfrak{ \: Now,\: }} \\ \\ \: \: \: \: \: \: \: \tt{ \purple{\angle CDA + w = 180 \degree }} \\ \\ \tt{ \purple{\implies 100 \degree+ w = 180 \degree }} \\ \\ \tt{ \purple{ \implies w = 180 \degree - 100 \degree}} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ \purple{ \therefore \: \: \underline{ \: \: \: w = 80 \degree\: }}}$

$\bold{\therefore \: \: \red{ x + y + z + w }} \\ \\ \bold{ = \red{ 60 \degree + 100 \degree + 120 \degree + 80 \degree }} \\ \\ \bold{ = \red{360 \degree }}$