Question

Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. FInd the measure of each angle.

Answer 1

`\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^(\circ) \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = (165)/(11)\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^(\circ)~ \text{and the smaller angle is }15^(\circ)`