Question

Someone help me with this question!

Answer 1

`\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°

Answer 2

Answer:
`160^(\circ)`

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)`