student needed to find the measure of angle b. He incorrectly said m angle b equals 128 degrees. Find the correct measure of angle b. What mistake did he likely​ make?

Question

b
52
a
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Question content area bottom
Part 1
manglebequals
  
38degrees
Part 2
What mistake did he likely​ make?
A.
He subtracted 52degrees from 180degrees instead of 90degrees.
B.
He subtracted 52degrees from 90degrees instead of 180degrees.
C.
He added 52degrees to 180degrees instead of 90degrees.
D.
He added 52degrees to 90degrees instead of 180degrees.

Answer 1

To resolve the student's mistake in finding the measure of angle \( b \), we need to understand the relationship between angles \( a \), \( b \), and the total degrees in a linear pair or a triangle, depending on their configuration.

Let's analyze the situation:

If \( m \angle b = 128^\circ \), and the correct measure of \( b \) is \( 38^\circ \), we can deduce that \( a + b = 180^\circ \) or \( a + b = 90^\circ \).

Given \( m \angle a = 52^\circ \), we can use the following relationships:

1. If \( a + b = 180^\circ \): \[ 52^\circ + m \angle b = 180^\circ \] \[ m \angle b = 180^\circ - 52^\circ = 128^\circ \] This would confirm the incorrect answer, as it suggests that the measure of angle \( b \) is indeed \( 128^\circ \).

2. If \( a + b = 90^\circ \): \[ 52^\circ + m \angle b = 90^\circ \] \[ m \angle b = 90^\circ - 52^\circ = 38^\circ \] This matches the correct measure of angle \( b \).

From this analysis, it appears the student likely interpreted the angles incorrectly and treated them as if they summed to \( 180^\circ \) when they were actually meant to sum to \( 90^\circ \).

Conclusion

The correct option explaining his mistake is:

B. He subtracted 52 degrees from 90 degrees instead of 180 degrees.

He mistakenly used a triangle sum (180 degrees) for a right angle setup (90 degrees).