in the triangle ABC, the measure of angle b=21 more than three times the measure of angle A. the measure of angle C=54 more than the measure of angle A. find the measure of each angle
The sum of the three angles is 180deg
b=21+a
c=54+a
add a+b+c and set = to 180
To find the measures of each angle in triangle ABC, let's assign a variable to angle A.
Let's say the measure of angle A is x degrees.
According to the given information:
- Angle B is 21 more than three times the measure of angle A. Therefore, the measure of angle B is 3x + 21 degrees.
- Angle C is 54 more than the measure of angle A. Therefore, the measure of angle C is x + 54 degrees.
Now, we can set up an equation using the sum of angles in a triangle, which is 180 degrees:
x + (3x + 21) + (x + 54) = 180
Simplifying the equation:
5x + 75 = 180
Next, we will isolate the variable:
5x = 180 - 75
5x = 105
Then, solve for x:
x = 105 / 5
x = 21
Now that we have the value of x, we can find the measures of each angle:
Angle A = x = 21 degrees
Angle B = 3x + 21 = 3(21) + 21 = 84 degrees
Angle C = x + 54 = 21 + 54 = 75 degrees
So, the measure of angle A is 21 degrees, angle B is 84 degrees, and angle C is 75 degrees in triangle ABC.