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a )
Sum of the interior angles of any triangle equals 180° .
Thus :
[tex]angle \: A + angle \: B + angle \: C = 180° \\ [/tex]
[tex]35° + 3(x+2)° + 52° = 180°[/tex]
[tex]35° + 3x + 6° + 52° = 180°[/tex]
[tex]3x + 93° = 180°[/tex]
Subtract sides 93°
[tex]3x + 93° - 93° = 180° - 93°[/tex]
[tex]3x = 87°[/tex]
Divide sides by 3
[tex] \frac{3x}{3} = \frac{87}{3} \\ [/tex]
[tex]x = 29°[/tex]
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b )
[tex]angle \: C = 3 ( x + 2 ) °[/tex]
[tex]angle \: C = 3 ( 29+ 2 ) °[/tex]
[tex]angle \: C = 3 ( 31 ) °[/tex]
[tex]angle \: C =93 °[/tex]
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