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 59°. what error might the student have made? a. the student only subtracted the right angle from 180°. b. the student subtracted the sum of the two given angles from 360°. c. the student only subtracted the acute angle from 180°. d. the student added the right angle and the given acute angle, but did not subtract the sum from 180°.

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°. Let the given acute angle be \(A = 31^{\circ}\) and the unknown acute angle be \(B\).

Step2: Calculate the unknown acute angle

We know that \(90^{\circ}+A + B=180^{\circ}\). Substituting \(A = 31^{\circ}\), we get \(B=180^{\circ}-90^{\circ}-31^{\circ}=59^{\circ}\).

Step3: Analyze the student's error

The student got 140°. If we assume the student subtracted the sum of the two given angles from 360°, \((90 + 31)=121\), and \(360-121 = 239
eq140\). If the student only subtracted the right - angle from 180°, \(180 - 90=90
eq140\). If the student only subtracted the acute angle from 180°, \(180 - 31 = 149
eq140\). If the student added the right - angle and the given acute angle \((90 + 31)=121\) and did not subtract from 180°, this is not related to getting 140°. But if we consider the error of subtracting the sum of the two given angles from 360°, it is the most likely error as the student might have confused the angle - sum property of a triangle (180°) with the angle measure around a point (360°).

Answer:

The measure of the other acute angle is \(59^{\circ}\)
B. The student subtracted the sum of the two given angles from 360°