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astraxan [27]
1 year ago
11

So,some please help me with this question !

Mathematics
2 answers:
Tamiku [17]1 year ago
4 0

\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

neonofarm [45]1 year ago
4 0
<h3>Answer:  63 degrees  (choice A)</h3>

=============================================================

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

-----------

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

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