Question
A student needed to find the measure of angle b. She incorrectly said m angle b equals 118 degrees. Find the correct measure of angle b. What mistake did she likely make?
b
62
a
(The figure is not shown to scale.)
Question content area bottom
Part 1
manglebequals
28degrees
Part 2
What mistake did she likely make?
A.
She added 62degrees to 180degrees instead of 90degrees.
B.
She subtracted 62degrees from 180degrees instead of 90degrees.
C.
She added 62degrees to 90degrees instead of 180degrees.
D.
She subtracted 62degrees from 90degrees instead of 180degrees.
b
62
a
(The figure is not shown to scale.)
Question content area bottom
Part 1
manglebequals
28degrees
Part 2
What mistake did she likely make?
A.
She added 62degrees to 180degrees instead of 90degrees.
B.
She subtracted 62degrees from 180degrees instead of 90degrees.
C.
She added 62degrees to 90degrees instead of 180degrees.
D.
She subtracted 62degrees from 90degrees instead of 180degrees.
Answers
GPT-4o mini
To find the correct measure of angle b, we can assume that there is a relationship between angles a and b. From the information given, we can establish that angle a is 62 degrees.
If angle a and angle b are supplementary angles (that is, they add up to 180 degrees), the correct calculation would be:
\[
m\angle b = 180° - m\angle a = 180° - 62° = 118°
\]
If, however, angles a and b are complementary (which means they add up to 90 degrees), the calculation would be:
\[
m\angle b = 90° - m\angle a = 90° - 62° = 28°
\]
Since the student incorrectly calculated \( m\angle b \) to be 118 degrees, it seems she was operating under the false assumption that the angles were supplementary. The correct calculation shows that angle b should be 28 degrees, indicating that the angles are likely complementary.
Given this reasoning, the mistake the student likely made is:
**A. She added 62 degrees to 180 degrees instead of 90 degrees.**
This indicates that she mistakenly considered the angles to be supplementary instead of complementary.
If angle a and angle b are supplementary angles (that is, they add up to 180 degrees), the correct calculation would be:
\[
m\angle b = 180° - m\angle a = 180° - 62° = 118°
\]
If, however, angles a and b are complementary (which means they add up to 90 degrees), the calculation would be:
\[
m\angle b = 90° - m\angle a = 90° - 62° = 28°
\]
Since the student incorrectly calculated \( m\angle b \) to be 118 degrees, it seems she was operating under the false assumption that the angles were supplementary. The correct calculation shows that angle b should be 28 degrees, indicating that the angles are likely complementary.
Given this reasoning, the mistake the student likely made is:
**A. She added 62 degrees to 180 degrees instead of 90 degrees.**
This indicates that she mistakenly considered the angles to be supplementary instead of complementary.