Find the measure of an angle, if six times its complement is 12° less than twice its supplement: - IQ786

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Find the measure of an angle, if six times its complement is 12° less than twice its supplement:

Find the measure of an angle, if six times its complement is 12° less than twice its supplement:

48

96

24

None of these

Explanation

Let angle = $x$
Complement = $90 - x$ , Supplement = $180 - x$
Given:

$6(90 - x) = 2(180 - x) - 12 \ 540 - 6x = 360 - 2x - 12 \ 540 - 6x = 348 - 2x \ 192 = 4x Rightarrow x = 48$

$540 - 6 x = 360 - 2 x - 12$

$540 - 6 x = 348 - 2 x$

$192 = 4 x \Rightarrow x = 48$