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In TRIANGLE ABC, what is the value of x?

In TRIANGLE ABC What Is The Value Of X class=

Sagot :

Answer:[tex]70^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle BAC=112^{\circ}\\\angle BCM=(2x+12)^{\circ}\\\angle ABL=2x^{\circ}[/tex]

[tex]\angle ACB[/tex] is given by [tex]180^{\circ}-\angle BCM[/tex] as the angle around a straight line is [tex]180^{\circ}[/tex]

[tex]\therefore \angle BCA=180^{\circ}-2x^{\circ}-12^{\circ}\\\angle BCA=(168-2x)^{\circ}[/tex]

Also, using exterior angle property. We can write

[tex]\angle BCA+\angle BAC=\angle ABL[/tex]

Insert the values

[tex]\Rightarrow 168^{\circ}-2x^{\circ}+112^{\circ}=2x^{\circ}\\\Rightarrow 280=4x^{\circ}\\\Rightarrow x=70^{\circ}[/tex]

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