Question

Please help me with the first question!

Answer 1

`\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star`

`\qquad❖ \: \sf \: \angle C = 63 \degree`

`\textsf{ \underline{\underline{Steps to solve the problem} }:}`

`\qquad❖ \: \sf \:x + 4x + 12 + x=180°`

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

`\qquad❖ \: \sf \:6x + 12 = 180`

`\qquad❖ \: \sf \:6x = 180 - 12`

`\qquad❖ \: \sf \:6x = 168`

`\qquad❖ \: \sf \:x = 28 \degree`

Next,

`\qquad❖ \: \sf \: \angle C + \angle D + x = 180°`

`\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°`

`\qquad❖ \: \sf \: \angle C +4x = 180 - 5`

`\qquad❖ \: \sf \: \angle C +4(28) = 175`

( x = 28° )

`\qquad❖ \: \sf \: \angle C +112 = 175`

`\qquad❖ \: \sf \: \angle C = 175 - 112`

`\qquad❖ \: \sf \: \angle C = 63 \degree`

`\qquad \large \sf {Conclusion} :`

`\qquad❖ \: \sf \: \angle C = 63 \degree`