Question

error analysis: on a math test the students are given a right triangle. one of the acute angles has a measure of 31°. one student says that the measure of the other acute angle is 149°. what is the measure of the other acute angle? what error might the student have made? the measure of the other acute angle is

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°.

Step2: Calculate the measure of the other acute angle

Let the measure of the other acute angle be \(x\). We know that \(90^{\circ}+31^{\circ}+x = 180^{\circ}\). Then \(x=180^{\circ}-90^{\circ}-31^{\circ}\).
\[x = 59^{\circ}\]

Step3: Analyze the student's error

The student likely forgot that the triangle is a right - triangle and did not subtract the 90° right - angle from 180° when finding the other acute angle. Instead, they just subtracted 31° from 180° to get 149°, which is incorrect as an acute angle must be less than 90°.

Answer:

59