Question

Please help me with this problem​

Answer 1

The measures of angles A, B, and C are respectively 21°, 125°, and 34°

Explanation:

Equations

We are given some conditions applying to the internal angles on a triangle ABC.

The measure of angle A is 13 less than the measure of angle C.

The measure of angle B is 11 less than 4 times the measure of angle C

Let x = measure of angle C

The first conditions states:

`m\angle A = x-13`

The second conditions states:

`m\angle B = 4x-11`

The sum of all angles must be 180°, thus:

`x - 13 + 4x - 11 + x = 180`

Simplifying:

6x -24 = 180

Adding 24:

6x = 204

Dividing by 6:

x = 204/6

x = 34

`m\angle C = x = 34^\circ`

`m\angle B = 4x-11 = 4*34-11 = 125^\circ`

`m\angle A = x - 13 = 34 - 13 = 21^\circ`

The measures of angles A, B, and C are respectively 21°, 125°, and 34°