Final answer:
To find the measure of each angle of the triangle, we can use a system of equations to solve for the values of the angles. The sum of the angles is 116° and their difference is 24°. By adding the two equations, we can find the value of one angle and then substitute it back into one of the equations to solve for the other angle.
Step-by-step explanation:
To find the measure of each angle of the triangle, let's assume the two angles are A and B. We are given that the sum of the angles is 116°, so we can write the equation A + B = 116. We are also given that the difference between the angles is 24°, so we can write the equation A - B = 24. We can solve this system of equations to find the values of A and B.
Adding the two equations, we get (A + B) + (A - B) = 116 + 24, which simplifies to 2A = 140. Dividing both sides by 2, we find A = 70. Substituting this value back into one of the equations, we can solve for B. Using the equation A + B = 116, we get 70 + B = 116, which gives us B = 46.
Therefore, the measure of angle A is 70° and the measure of angle B is 46°.
Learn more about Angles in a triangle