Question
angle a and angle b are vertical angles and angle b is complementary to angle c. the measure of angle a is 22 degrees. what is the measure of angle c?
Answers
Answered by
GPT-4o mini
Since angles \( a \) and \( b \) are vertical angles, they are equal. Therefore, the measure of angle \( b \) is also \( 22^\circ \).
Given that angle \( b \) is complementary to angle \( c \), the sum of the measures of angles \( b \) and \( c \) is \( 90^\circ \).
We can express this relationship as:
\[
b + c = 90^\circ
\]
Substituting the value of angle \( b \):
\[
22^\circ + c = 90^\circ
\]
To find the measure of angle \( c \), we subtract \( 22^\circ \) from both sides:
\[
c = 90^\circ - 22^\circ
\]
Calculating this gives:
\[
c = 68^\circ
\]
Therefore, the measure of angle \( c \) is \( 68^\circ \).
Given that angle \( b \) is complementary to angle \( c \), the sum of the measures of angles \( b \) and \( c \) is \( 90^\circ \).
We can express this relationship as:
\[
b + c = 90^\circ
\]
Substituting the value of angle \( b \):
\[
22^\circ + c = 90^\circ
\]
To find the measure of angle \( c \), we subtract \( 22^\circ \) from both sides:
\[
c = 90^\circ - 22^\circ
\]
Calculating this gives:
\[
c = 68^\circ
\]
Therefore, the measure of angle \( c \) is \( 68^\circ \).