Question

what is ( mangle a )?
enter your answer in the box.
(the image shows a triangle with vertices a, b, c. angle at c is ( x^circ ), angle at a is ( (3x + 13)^circ ), angle at b is ( (x - 8)^circ ). there is a box for entering the answer and a numbering panel on the left with numbers 1,2,3,4,5 and a next button.)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(x + (3x + 13) + (x - 8) = 180\).

Step2: Simplify the equation

Combine like terms: \(x + 3x + x + 13 - 8 = 180\) → \(5x + 5 = 180\).

Step3: Solve for \(x\)

Subtract 5: \(5x = 175\) → \(x = 35\).

Step4: Find \(m\angle A\)

Substitute \(x = 35\) into \(3x + 13\): \(3(35) + 13 = 105 + 13 = 118\).

Answer:

\(118\)