To solve the problem of finding the value of \( x \) in each right angle, we need to use the concept of complementary angles. Two angles are complementary if their measures add up to 90 degrees. Let's solve each part step by step.
Problem 1:
Given: One angle is \( 45^\circ \).
Since the two angles form a right angle (90 degrees), we have:
\[
x + 45^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 45^\circ = 45^\circ
\]
So, \( x = 45^\circ \).
Problem 2:
Given: One angle is \( 72^\circ \).
Using the same logic:
\[
x + 72^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 72^\circ = 18^\circ
\]
So, \( x = 18^\circ \).
Problem 3:
Given: One angle is \( 2x \).
Since the two angles form a right angle:
\[
x + 2x = 90^\circ
\]
Simplifying:
\[
3x = 90^\circ
\]
Solving for \( x \):
\[
x = \frac{90^\circ}{3} = 30^\circ
\]
So, \( x = 30^\circ \).
Problem 4:
Given: One angle is \( 81^\circ \).
Using the same logic:
\[
x + 81^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 81^\circ = 9^\circ
\]
So, \( x = 9^\circ \).
Problem 5:
Given: One angle is \( 17^\circ \).
Using the same logic:
\[
x + 17^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 17^\circ = 73^\circ
\]
So, \( x = 73^\circ \).
Problem 6:
Given: One angle is \( 43^\circ \).
Using the same logic:
\[
x + 43^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 43^\circ = 47^\circ
\]
So, \( x = 47^\circ \).
Problem 7:
Given: One angle is \( 77^\circ \).
Using the same logic:
\[
x + 77^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 77^\circ = 13^\circ
\]
So, \( x = 13^\circ \).
Problem 8:
Given: One angle is \( 68^\circ \).
Using the same logic:
\[
x + 68^\circ = 90^\circ
\]
Solving for \( x \):
\[
x = 90^\circ - 68^\circ = 22^\circ
\]
So, \( x = 22^\circ \).
Final Answers:
\[
\boxed{45^\circ, 18^\circ, 30^\circ, 9^\circ, 73^\circ, 47^\circ, 13^\circ, 22^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of complementary and supplementary worksheet.
