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

Answer:

$16^\circ, 88^\circ, 76^\circ$

Step-by-step 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 = $5x+8 = 5 \times 16 + 8 = 80+8 = 88^\circ$

The third angle = $4x+12 = 4\times 16 + 12 = 76^\circ$

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