Question

One of the angles of a triangle is 8 deg more than 5 times another angle. If the third angle is 4 deg larger than the difference of the first two angles, find the angles.

Answer 1

`16^\circ, 88^\circ, 76^\circ`

Explanation:

Given a triangle.

One of the angles is
`8^\circ` more than 5 times of one angle.

Third angle is
`4^\circ` more than the difference of two angles.

To find:

The angles.

Solution:

Let the first angle =
`x^\circ`

As per question statement, second angle = 5
`x^\circ` +
`8^\circ`

And third angle = 5
`x^\circ` +
`8^\circ` -
`x^\circ` +
`4^\circ` =
`(4x+12)^\circ`

Using triangle sum property that the sum of all the internal angles of a triangle is always equal to
`180^\circ`.

`x+5x+8+4x+12 = 180\\\Rightarrow 10x+20=180\\\Rightarrow 10x = 160\\\Rightarrow x = 16`

Therefore, the first angle =
`x^\circ = 16^\circ`

The second angle =
`5x+8 = 5 * 16 + 8 = 80+8 = 88^\circ`

The third angle =
`4x+12 = 4* 16 + 12 = 76^\circ`

Therefore, the angles are
`16^\circ, 88^\circ, 76^\circ`.