Question

The angles of a triangle are described as follows: Angle A is the largest angle; it’s measure is twice the measure of Angle B. The measure of Angle C is 10 more than one-third of Angle B. Find the measures of the three angles in degrees. Remember, a triangle’s angles sum to 180°. Angle A = _______ Angle B= _______ Angle C = _______

Answer 1

Angle A = 102 degrees, Angle B = 51 degrees, Angle C = 27 degrees

Step-by-step explanation:

To solve this problem, we can use algebraic equations to represent the relationships between the angles. Let's assign a variable to Angle B, such as x. We know that Angle A is twice the measure of Angle B, so Angle A can be represented as 2x. Angle C is 10 more than one-third of Angle B, so Angle C can be represented as (1/3)x + 10.

The sum of all the angles in a triangle is 180 degrees, so we can set up the equation 2x + x + (1/3)x + 10 = 180. Simplifying the equation, we get 6x + 3x + x + 30 = 540. Combining like terms, we have 10x + 30 = 540. Subtracting 30 from both sides gives us 10x = 510. Dividing both sides by 10, we find that x = 51.

Now that we know the value of x, we can substitute it back into the equations to find the measures of the angles. Angle A = 2x = 2(51) = 102 degrees. Angle B = x = 51 degrees. Angle C = (1/3)x + 10 = (1/3)(51) + 10 = 17 + 10 = 27 degrees.