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° )

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

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

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

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

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