Respuesta :

Answer:  63 degrees  (choice A)

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Explanation:

Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.

Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.

So,

(angleEBA) + (angleEBD) + (angleDBC) = 180

( x ) + (4x+12) + (x) = 180

(x+4x+x) + 12 = 180

6x+12 = 180

6x = 180-12

6x = 168

x = 168/6

x = 28

Angles EBA and DBC are 28 degrees each.

This means angle D = 3x+5 = 3*28+5 = 89

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Then we have one last set of steps to finish things off.

Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.

D+B+C = 180

89 + 28 + C = 180

117+C = 180

C = 180 - 117

C = 63 degrees

GʀɪᴍRᴇᴀᴘᴇʀ

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]

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

[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]

[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]

[tex]\qquad❖ \: \sf \:6x = 168[/tex]

[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]

( x = 28° )

[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

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