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: $160^{\circ}$

Step-by-step explanation:

By the exterior angle theorem,

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