The sum of the angles of a triangle is 180 degrees. In the figure below angle B and angle C are the same size. If angle A is 54 degrees smaller than angle B. Find the measure of each angle.
(x - 54) + 2x = 180
To solve this problem, we can start by assigning variables to the unknown angles. Let's call the measure of angle B as 'x'.
According to the information given, angle A is 54 degrees smaller than angle B. So, we can express the measure of angle A as 'x - 54'.
Next, we know that angle C is the same size as angle B. So, the measure of angle C is also 'x'.
According to the property of a triangle, the sum of the angles of a triangle is 180 degrees. Therefore, we can write the following equation:
Angle A + Angle B + Angle C = 180
Substituting the expressions for the angles with the given information, we have:
(x - 54) + x + x = 180
Simplifying the equation, we combine like terms:
3x - 54 = 180
Add 54 to both sides of the equation:
3x = 234
Divide both sides of the equation by 3:
x = 78
Now that we have found the value of 'x', we can substitute it back into the expressions for Angle A and Angle C to find their measurements.
Angle A = x - 54 = 78 - 54 = 24 degrees
Angle B = x = 78 degrees
Angle C = x = 78 degrees
Therefore, the measure of each angle is:
Angle A = 24 degrees
Angle B = 78 degrees
Angle C = 78 degrees