One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles of the triangle is $4 : 5$ , find the angles of the triangle.

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Solution

Let the measure of other two angles be $4 x$ and $5 x$ .
It is given that one of the angles is equal to sum of other two angles i.e. $4 x + 5 x$ .
Sum of the angles is $180^{o}$ .
Therefore, $4 x + 5 x + 4 x + 5 x = 180$
$18 x = 180$
$x = 10$
Therefore, angles of a triangle are $4 x = 40$ , $5 x = 50$ and $4 x + 5 x = 90$ .

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One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles of the triangle is 4:5, find the angles of the triangle.

Let the measure of other two angles be 4x and 5x.It is given that one of the angles is equal to sum of other two angles i.e. 4x+5x.Sum of the angles is 180o.Therefore, 4x+5x+4x+5x=18018x=180x=10Therefore, angles of a triangle are 4x=40, 5x=50 and 4x+5x=90.

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