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shusha [124]
1 year ago
5

Someone help me with this question!

Mathematics
2 answers:
siniylev [52]1 year ago
8 0

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

  • Angle BCA = 160°

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

By Exterior angle property :

\qquad❖ \:  \sf   \:4x - 114 + 5x - 182 = 5x - 100

\qquad❖ \:  \sf   \:9x -29 6 = 5x - 100

\qquad❖ \:  \sf   \:9x - 5x =  - 100 + 296

\qquad❖ \:  \sf   \:4x = 96

\qquad❖ \:  \sf   \:x = 24 \degree

Next, Angle BCA = 180° - Angle BCD

( linear pair )

[ let angle BCA = y ]

\qquad❖ \:  \sf   \:y = 180 - (5x- 100)

\qquad❖ \:  \sf   \:y = 180 - (5(24) - 100)

\qquad❖ \:  \sf   \:y = 180 - (120 - 100)

\qquad❖ \:  \sf   \:y = 180 - 20

\qquad❖ \:  \sf   \:y = 160 \degree

\qquad \large \sf {Conclusion}  :

  • Angle BCA = 160°
VMariaS [17]1 year ago
6 0

Answer: 160^{\circ}

Step-by-step explanation:

By the exterior angle theorem,

4x-14+5x-182=5x-100\\\\9x-196=5x-100\\\\4x=96\\\\x=24\\\\\implies m\angle BCD=20^{\circ}\\\\\implies m\angle BCA=160^{\circ}

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