Question

Triangle abc has the following angle measures: m∠a = (2x - 24)°, m∠b = (x + 8)°, m∠c = (4x + 49)°. What is the measure of angle a?

1) 18°
2) 21°
3) 29°
4) 133°

Answer 1

Upon solving for x using the sum of angles in a triangle, angle A's measure is calculated as 34 degrees, which is not included in the given options, suggesting an error in the question.

Step-by-step explanation:

The problem stated involves finding the measure of angle A in a triangle with given algebraic expressions for its angles. The sum of the angles in any triangle is 180 degrees, which is a fundamental rule in geometry. Using this rule, we can set up an equation that sums the provided expressions for each angle to 180 degrees: (2x - 24) + (x + 8) + (4x + 49) = 180. Solving for x, we get x = 29 degrees. Substituting the value of x back into the expression for angle A (2x - 24), we find the measure of angle A to be 34 degrees, which is not present in the provided options, indicating a possible typo in the question or options.