Ratio, SM-Bank 026

It is known that one of the angles in a triangle is \(120^{\circ}\).

Calculate the size of the other 2 angles if they are in the ratio \(2:3\). (3 marks)

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\(24^{\circ}\ \text{and}\ 36^{\circ}\)

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\(\text{Angle sum of a triangle}=180^{\circ}\)

\(\therefore\ \text{Remaining angles}=180-120=60^{\circ}\)

\(\text{Total parts remaining angles}=2+3=5\)

\(\text{1st angle}=\dfrac{2}{5}\times 60=24\)

\(\text{2nd angle}=\dfrac{3}{5}\times 60=36\)

\(\therefore\ \text{The remaining angles are}\ 24^{\circ}\ \text{and}\ 36^{\circ}.\)