Question 966014: The measures of the angles of a triangle are in the ratio of 1 : 3 : 5. Find the measure of the largest angle. Answer by ikleyn(52777) (Show Source):
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Let x be the measure of the first, the smallest angle of the triangle, in degrees.
Then the measure of the second angle is 3x degrees, and the measure of the third angle is 5x degrees.
In total, the sum of these three angles of the triangle is x + 3x + 5x = 9x degrees.
From the other side, as you know, the sum of interior angles of any triangle is 180°.
It gives you an equation
9x = 180°.
Hence, x = = 20°.
Answer. The smallest angle of the triangle is 20°. Two other angles are of 60° and 100°. The largest angle is of 100°.
