Final answer:
To find the measure of each angle in the triangle, assign a variable to angle A. Use the given information to set up an equation. Simplify and solve for A, then substitute the value of A in angle R and angle T.
Step-by-step explanation:
To find the measure of each angle in the triangle, we can use the given information. Let's assign a variable to the measure of angle A. We know that angle R is 3 times the measure of angle A, so angle R = 3A. We also know that angle T is 70° more than angle A, so angle T = A + 70°. Since the sum of the measures of the angles of a triangle is 180°, we can write the equation: A + 3A + (A + 70°) = 180°.
Simplifying the equation, we get: 5A + 70° = 180°. Subtracting 70° from both sides, we have: 5A = 110°. Dividing both sides by 5, we find that A = 22°. Substituting the value of A back into angle R and angle T, we get: angle R = 3(22°) = 66°, and angle T = 22° + 70° = 92°. Therefore, the measure of angle A is 22°, the measure of angle R is 66°, and the measure of angle T is 92°. The question involves solving for the measures of angles in a triangle using the properties that the sum of angles in a triangle is 180° and the algebraic expressions that define the relationships between the angles. Let the measure of angle A be x degrees. According to the problem, the measure of angle R is 3 times the measure of angle A, so angle R can be expressed as 3x degrees. Similarly, the measure of angle T is 70° more than the measure of angle A, giving us the expression for angle T as x + 70°. To find the measures of each angle, we can write the equation x + 3x + (x + 70°) = 180°. Simplifying, we get 5x + 70° = 180°. Subtracting 70° from both sides, we have 5x = 110°. Dividing both sides by 5, we find x = 22°. With this value, we can determine the measures of angles R and T. Angle R, being 3 times angle A, is 66° and angle T, being 70° more than angle A, is 92°.