Short Answer 
The angles in Triangle ABC are expressed in terms of a variable x, resulting in the equations 2x, 5x, and 11x. By setting the sum of these angles equal to 180 degrees, we find x = 10, which leads to the measures of the angles being 20 degrees for angle A, 50 degrees for angle B, and 110 degrees for angle C.
Step 1: Establish the Sum of Angles in a Triangle
In any triangle, the sum of the interior angles is always equal to 180 degrees. For Triangle ABC, we are provided angle measures expressed in terms of a variable, x. The angles are:
- Measure of angle A = (2x) degrees
- Measure of angle B = (5x) degrees
- Measure of angle C = (11x) degrees
Step 2: Create an Equation from the Angle Measures
To find the value of x, we need to sum all angles and set it equal to 180 degrees. This can be represented as:
- Angle A + Angle B + Angle C = 180
- 2x + 5x + 11x = 180
Combining like terms gives us 18x = 180, leading to x = 10 degrees.
Step 3: Calculate Each Angle’s Measure
With the value of x now known, we can determine each angle’s measure:
- Angle A = 2x = 2 √ó 10 = 20 degrees
- Angle B = 5x = 5 √ó 10 = 50 degrees
- Angle C = 11x = 11 √ó 10 = 110 degrees
Thus, the correct option from the choices given is: a) Measure of angle A = 20 degrees.