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:

[tex]16^\circ, 88^\circ, 76^\circ[/tex]

Step-by-step explanation:

Given a triangle.

One of the angles is [tex]8^\circ[/tex] more than 5 times of one angle.

Third angle is [tex]4^\circ[/tex] more than the difference of two angles.

To find:

The angles.

Solution:

Let the first angle = [tex]x^\circ[/tex]

As per question statement, second angle = 5[tex]x^\circ[/tex] + [tex]8^\circ[/tex]

And third angle = 5[tex]x^\circ[/tex] + [tex]8^\circ[/tex] - [tex]x^\circ[/tex] + [tex]4^\circ[/tex] = [tex](4x+12)^\circ[/tex]

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

[tex]x+5x+8+4x+12 = 180\\\Rightarrow 10x+20=180\\\Rightarrow 10x = 160\\\Rightarrow x = 16[/tex]

Therefore, the first angle = [tex]x^\circ = 16^\circ[/tex]

The second angle = [tex]5x+8 = 5 \times 16 + 8 = 80+8 = 88^\circ[/tex]

The third angle = [tex]4x+12 = 4\times 16 + 12 = 76^\circ[/tex]

Therefore, the angles are [tex]16^\circ, 88^\circ, 76^\circ[/tex].

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