2
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Matrices — Test

Question 2 • Algebra II

Ming drew a triangle. The sum of the angles of the triangle is 180 degrees In Ming’s triangle, angle cap b is twice the measure of angle cap A , and angle angle cap c is 5 degrees greater than four times angle cap A The system of equations can be used to find the measure of the three angles, where a represents the measure of angle cap A , b represents the measure of angle cap b , and c represents the measure of angle cap c A plus b plus c is equal to 180 2 A is equal to b 4 A plus 5 is equal to c Which matrix represents the measure of each angle in Ming’s triangle?

Answer
A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 25 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 50 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 105
B
[11102−10040−10]
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 45 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, negative 45 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 180
D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 1 column 3, 0 column 4, 75 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 50 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 105

Explanation

Substitute b = 2a and c = 4a + 5 into a + b + c = 180: a + 2a + 4a + 5 = 180. Thus 7a = 175, so a = 25; then b = 50 and c = 105. Choice A is the matrix that shows these angle measures: 25°, 50°, and 105°.

AI-written and checked against the verified answer.

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