Question

the measure of an angle which is 24° more then it's complement is A) 156° B) 57° C) 114° D) 66°​

Answer 1

$\huge \sf \underline \red{Answer : }$

$\sf \underline{ \therefore \: x = 57 \:(b)}$

$\huge \sf \underline \blue{Given : }$

• An angle is 24 degrees more than its complement

$\huge \sf \underline \pink{solution : }$

$\sf \underline{Let \: the \: angle \: be \: x}$

$\sf \underline{so \: complement \: angle \: will \: be \: (x - 24)}$

$\sf \underline{we \: know \: that : }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \tt{sum \: of \: angle = 90 \: }}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{x + (x - 24) = 90}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{2x - 24= 90}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{2x = 90 + 24}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{2x = 114}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{x = \dfrac{114}{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \normalsize{= {\cancel{\dfrac{114}{2}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⤑{x = 57}$

$\sf \underline{ \therefore \: x = 57}$

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• The angle which is 24 degree more than its complement is 57 (b)