Question

error analysis on a math test the students are given a right triangle. one of the acute angles has a measure of 43°. one student says that the measure of the other acute angle is 137°. what is the measure of the other acute angle? what error might the student have made?

Explanation:

Step1: Recall angle - sum property of a right - triangle

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°. Let the two acute angles be \(A\) and \(B\). So, \(A + B+90^{\circ}=180^{\circ}\), which simplifies to \(A + B = 90^{\circ}\).

Step2: Calculate the measure of the other acute angle

Given one acute angle \(A = 43^{\circ}\). Let the other acute angle be \(B\). Then \(B=90^{\circ}-43^{\circ}\).
\(B = 47^{\circ}\)

Step3: Analyze the student's error

The student said the other acute angle is \(137^{\circ}\). The error is that the student likely forgot that the sum of the two acute angles in a right - triangle is 90°. An angle of \(137^{\circ}\) is an obtuse angle, and a right - triangle can only have two acute angles and one right angle.

Answer:

47; The student likely forgot that the sum of the two acute angles in a right - triangle is 90° and gave an obtuse - angle value instead of an acute - angle value.