In triangle ABC, the measure of angle B is 27 degrees more than three times the measure of angle A. The measure of angle C is 48 degrees more than the measure of angle A. Find the measure of each angle.

angle A --- x

angle B --- 3x+27
angle C --- x+48

you know the sum of those three is 180°

take it from there

To find the measure of each angle in triangle ABC, let's say the measure of angle A is x degrees.

According to the given information, the measure of angle B is 27 degrees more than three times the measure of angle A. So, angle B can be expressed as 3x + 27.

Similarly, the measure of angle C is 48 degrees more than the measure of angle A. Therefore angle C can be expressed as x + 48.

Since the sum of all angles in a triangle is always 180 degrees, we can write the equation:

A + B + C = 180

Substituting the expressions for angles A, B, and C, we have:

x + (3x + 27) + (x + 48) = 180

Now we can solve this equation to find the value of x:

5x + 75 = 180
5x = 180 - 75
5x = 105
x = 105 / 5
x = 21

So, angle A is 21 degrees.

Now we can find the measure of angles B and C:

Angle B = 3x + 27 = 3(21) + 27 = 63 + 27 = 90 degrees.

Angle C = x + 48 = 21 + 48 = 69 degrees.

Therefore, the measure of angle A is 21 degrees, angle B is 90 degrees, and angle C is 69 degrees in triangle ABC.