# The angles of a triangle are equal to 4x + 30, 2x – 10 and 6x . What are the angles of the triangle?

hala718 | Certified Educator

Let us assume that the angle ABC.

We will also assume that A, B, and C are angles such that:

==> A = 4x + 30

==> B = 2x - 10

==> C = 6x.

But we know that the sum of the triangle's angles is 180.

==> A + B + C = 180.

==> (4x + 30) + ( 2x - 10) + 6x = 180

We will combine like terms.

==> 12x + 20 = 180

Subtract 20 from both sides.

==> 12x = 160

Now we will divide by 12.

==> x = 160 / 12 = 40/3

==> x = 40/3

==> A = 4x + 30 = 4*40/3  + 30 = 160/3 + 30= 250/3 degrees

==> B = 2x - 10 = 2*40/3 -10 = 80/3 - 10 = 50/3 degrees

==> c = 6x = 6*40/3 = 80 degrees.

Then the angles of the triangle are:

250/3 degrees, 50/3 degrees, and 80 degrees.

justaguide | Certified Educator

The sum of the three angles of a triangle is equal to 180 degree.

Now the angles of the triangle are given as 4x + 30, 2x – 10 and 6x.

=> 4x + 30 + 2x – 10 + 6x = 180

=> 4x + 2x + 6x + 30 – 10 = 180

=> 12x = 180 – 30 +10

=> 12x = 160

=> x = 160/12

=> x= 40/ 3 degrees

Therefore the angles of the triangle are

4*40/3 + 30 = 250/3

2*40/3 – 10 = 50/3

6*40/3 = 80

Therefore the required angles are 250/3, 50/3 and 80 degrees.