Question 482547


Since angles P & Q are supplementary, then P + Q = 180


Since angle Q is 10 less than 4 times angle P, then we can say that: Q = 4P – 10 ------ - 4P + Q = - 10


     P + Q  = 180 -------- eq (i) 
– 4P + Q = - 10 --------- eq (ii)
  4P + 4Q = 720 ------- eq (iii) -------- Multiplying eq (i) by 4
5Q = 710 ------ Adding eq (ii) and (iii)
Angle Q = {{{710/5}}} = {{{highlight_green(142^o)}}}


Substituting 142 for Q in eq (i) results in: P + 142 = 180


Angle P = 180 – 142 = {{{highlight_green(38^0)}}}


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Check
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Angle Q = {{{142^o}}}  

Angle P = {{{38^o}}}, so 4 times angle P = 4 * 38 = {{{152^o}}}


It can be seen that angle Q ({{{142^o}}}) is 10 less than 4 times angle P ({{{152^o}}})


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