Question

in a triangle the second angle is 1/6 of the third angle and the third angle is three times of first angle then find all the angles of the triangle​ let the angles of the triangle be x y z respectively​

Answer 1

Answer:

We can create a system of equations where x is the first, y the second, and z the third, knowing that all triangles sum to 180 degrees.

y = 3x

z = 2y

x + y + z = 180.

Substitute into the last equation to get:

x + 3x + 2y = 180, 2y = 2(3x), so 2y = 6x. Which makes it

x + 3x + 6x = 180

10x = 180. x = 18. Use x to find y:

y = 3(18)

y = 54 degrees.

Use y to find z.

z = 2(54)

z = 108.

Now, make sure this works: 18+54+108 = 180, so yes, this does form a triangle.

So the three angles are 18 degrees, 54 degrees, and 108 degrees.