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.