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In a certain triangle, the measure of angle A is three times as big as the measure of angle C and the
measure of angle B is 55 degrees bigger than the measure of angle C. What is the degree measure of angle
A?
1
I
X

Answer 1

In a certain triangle, angle A is three times angle C and angle B is 55 degrees bigger than angle C. By setting up an equation and solving for x, we find that angle C is 25 degrees. Therefore, angle A is 75 degrees.

Step-by-step explanation:

Let's assign a variable to the measure of angle C. We can call it x. According to the problem, angle A is three times as big as angle C, so angle A can be represented as 3x. And angle B is 55 degrees bigger than angle C, so angle B can be represented as x + 55.

We know that in a triangle, the sum of the angles is always 180 degrees. So we can set up the equation: x + 3x + (x + 55) = 180. Simplifying this equation, we get 5x + 55 = 180. Subtracting 55 from both sides, we get 5x = 125. Dividing both sides by 5, we find that x = 25.

Now we can find the measure of angle A by substituting x = 25 into our equation 3x. Angle A = 3(25) = 75 degrees.

Learn more about Triangle angles