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
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Part 1
manglebequals
enter your response heredegrees
b
62
a
(The figure is not shown to scale.)
Question content area bottom
Part 1
manglebequals
enter your response heredegrees
Answers
GPT-4o mini
To determine the correct measure of angle \( b \) and identify the student's mistake, we need to consider the triangle angle sum theorem, which states that the sum of the angles in a triangle is always \( 180^\circ \).
From the information provided, it appears that angle \( b \) is one of the angles in a triangle and that the other angle (labeled \( a \)) measures \( 62^\circ \).
To find the correct measure for angle \( b \), we can use the following equation based on the triangle angle sum theorem:
\[
m\angle a + m\angle b + m\angle c = 180^\circ
\]
If the total of angle \( a \) and angle \( b \) equals \( 118^\circ \), then angle \( c \) must be calculated:
\[
m\angle a + m\angle b + m\angle c = 180^\circ
\]
Assuming angle \( c \) is the remaining angle:
\[
62^\circ + m\angle b + m\angle c = 180^\circ
\]
If we set \( m\angle c = 180^\circ - 118^\circ \) to isolate angle \( b \):
\[
m\angle b = 180^\circ - (62^\circ + 118^\circ)
\]
\[
m\angle b = 180^\circ - 118^\circ
\]
\[
m\angle b = 62^\circ
\]
The student likely made the mistake of assuming that two angles' measures (including angle \( b \)) added up to \( 118^\circ \), instead of correctly considering the angle sum of all angles in the triangle.
So the correct measure of angle \( b \) is:
\[
m\angle b = 62^\circ
\]
From the information provided, it appears that angle \( b \) is one of the angles in a triangle and that the other angle (labeled \( a \)) measures \( 62^\circ \).
To find the correct measure for angle \( b \), we can use the following equation based on the triangle angle sum theorem:
\[
m\angle a + m\angle b + m\angle c = 180^\circ
\]
If the total of angle \( a \) and angle \( b \) equals \( 118^\circ \), then angle \( c \) must be calculated:
\[
m\angle a + m\angle b + m\angle c = 180^\circ
\]
Assuming angle \( c \) is the remaining angle:
\[
62^\circ + m\angle b + m\angle c = 180^\circ
\]
If we set \( m\angle c = 180^\circ - 118^\circ \) to isolate angle \( b \):
\[
m\angle b = 180^\circ - (62^\circ + 118^\circ)
\]
\[
m\angle b = 180^\circ - 118^\circ
\]
\[
m\angle b = 62^\circ
\]
The student likely made the mistake of assuming that two angles' measures (including angle \( b \)) added up to \( 118^\circ \), instead of correctly considering the angle sum of all angles in the triangle.
So the correct measure of angle \( b \) is:
\[
m\angle b = 62^\circ
\]