the measures of the angles of LMN are in the ratio 1:2:5. what are the measurements of the angles

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06-09-2018
Mathematics

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the measures of the angles of LMN are in the ratio 1:2:5. what are the measurements of the angles

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highwireact highwireact · Answer 1 · 2018-09-06T03:38:47+02:00

I assume LMN here refers to a triangle, in which case we know that its interior angles have to add to 180°. What this ratio is saying is that, if we split that 180 up into some number of pieces, one of the angles is going to take up 1 of those pieces, one is going to take up 2 pieces, and one is going to take up 5 pieces. How many pieces did we split the 180 up into the first place? Adding up all of the pieces, we find that the number is 1 + 2 + 5 = 8.

Splitting 180 up 8 ways makes the value of each piece 180 ÷ 8 = 22.5, so the measures of our angles are

1 × 22.5 = 22.5°,
2 × 22.5 = 45°, and
5 × 22.5 = 112.5°