LET THE GREATER ANGLE BE x SINCE x IS 45 DEGREES LESS THAN TWO TIMES OF ITS SUPPLEMENT THEREFORE x+45=2(180-x) =>x+45=360-2x =>x+2x=360-45 =>3x=315 =>x=315/3 =>x=105 ANS. GREATER ANGLE IS 105
The supplements would be- x degree and 2x-45 degree. We all know that two supplements together measure 180 degrees. So, we have- x+2x-45=180 =3x-45=180 =3x=180+45 (On Transposing -45 to RHS becomes+45) =3x=225 =x=225/3 (On Transposing *3 to RHS becomes /3) =x=75 degrees (This is the first angle) So, 2nd angle= 2x-45= 2*75-45= 150-45= 105 degrees On checking, we have 105+75=180 degrees. So greater angle measures 105 degrees.(Answered and proved with explanation).
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