in a triangle abc, the measure of angle b is 34 degrees more than three times the measure of angle a. the measure c is 56 degrees more than the angle a. what is the measure of each angle

b = 3a +34º, c = a + 56º

a + (3a+34º) + (a+56º) = 180º

Solve for a, then the other angles.

Let's say the measure of angle A is "x" degrees.

According to the given information, the measure of angle B is 34 degrees more than three times the measure of angle A, so angle B can be represented as (3x + 34) degrees.

Similarly, the measure of angle C is 56 degrees more than the angle A, so angle C can be represented as (x + 56) degrees.

According to the properties of a triangle, the sum of the measures of the angles of a triangle is always 180 degrees.

Therefore, the equation for the sum of the angles in triangle ABC can be written as:

x + (3x + 34) + (x + 56) = 180

Simplifying the equation:

5x + 90 = 180

Subtracting 90 from both sides:

5x = 90

Dividing both sides by 5:

x = 18

So, angle A is 18 degrees.

Using this value, we can find the measures of angles B and C:

Angle B = 3x + 34 = 3(18) + 34 = 54 + 34 = 88 degrees

Angle C = x + 56 = 18 + 56 = 74 degrees

Therefore, the measures of angles A, B, and C are 18 degrees, 88 degrees, and 74 degrees, respectively.

To find the measure of each angle in triangle ABC, let's assign variables to the angles.

Let's say angle A = x degrees.
Therefore, angle B = 3x + 34 degrees, as it is 34 degrees more than three times the measure of angle A.
Angle C = x + 56 degrees, as it is 56 degrees more than the angle A.

Now, let's use the fact that the sum of all angles in a triangle is equal to 180 degrees.

x + (3x + 34) + (x + 56) = 180
5x + 90 = 180
5x = 180 - 90
5x = 90
x = 90 / 5
x = 18

Now, we can substitute the value of x back into the expressions to find the measures of the angles:

Angle A = x = 18 degrees
Angle B = 3x + 34 = 3(18) + 34 = 54 + 34 = 88 degrees
Angle C = x + 56 = 18 + 56 = 74 degrees

Therefore, the measure of angle A is 18 degrees, angle B is 88 degrees, and angle C is 74 degrees in triangle ABC.