Question

In angle ABC the measure of Angle B is 13 more than the measure of Angle A and the measure of angle C is 9 less than twice the measure of angle A find the measure of each angle in ABC. only an algebraic will be accepted.

Answer 1

By establishing a variable for the smallest angle and applying the sum of angles in a triangle equals 180 degrees, we determined the measures of the angles in triangle ABC to be Angle A: 44 degrees, Angle B: 57 degrees, and Angle C: 79 degrees.

Step-by-step explanation:

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees. Let's denote the measure of Angle A by the variable 'a'. According to the problem, Angle B can be represented as 'a + 13' and Angle C can be approximated as '2a - 9'. By adding these expressions together, we get:

a + (a + 13) + (2a - 9) = 180

Combining like terms, we get:

4a + 4 = 180

Subtracting 4 from both sides gives us:

4a = 176

Dividing both sides by 4 gives us the value of a:

a = 44

Now we can find the measure of Angle B and Angle C:

Angle B = a + 13 = 44 + 13 = 57 degrees

Angle C = 2a - 9 = 2(44) - 9 = 79 degrees

Therefore, the measures of the angles in triangle ABC are Angle A: 44 degrees, Angle B: 57 degrees, and Angle C: 79 degrees.