Question

if one angle of a triangle is equal to the sum of the other two angle also one of the angle is one third of the largest angle find the angles of a triangle.

Answer 1

let the three angles of triangle be

x , y , and z.

one angle = sum of other 2 Angles

x = y + z ---(1)

let y = 1/ 3rd of the largest angle

y = 1/ 3 rd of x = x / 3

y = x / 3. ---(2)

sum of all the angles of triangle = 180°

x + y + z = 180°

x + x / 3 + z = 180

3x + x + 3z = 540

4x + 3z = 540 -------(3)

from (1) x = y + z =>

z = x - y = x - x / 3 = 2x/ 3

thus z = 2x / 3 ------(4)

put value of z in eq.(3), we get

4x + 3( 2x/ 3) = 540

6x = 540 => x = 90°

from(2)

y = x / 3 = 90 / 3 = 30°

from(4)

z = 2x / 3 = 2(90)/ 3 = 60°

therefore, x = 90° , y = 30° , z = 60°

Answer:
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all the angles of triangle are 90°, 30° and 60°.