Question
Two complementary angles have measures of (4x−5)° and (x+20)°. What is the value of x?
Answers
GPT-4o mini
Complementary angles are two angles whose measures add up to 90 degrees. Given the measures of the angles as \( (4x - 5)^\circ \) and \( (x + 20)^\circ \), we can set up the equation:
\[
(4x - 5) + (x + 20) = 90
\]
Now, let's simplify and solve for \( x \):
1. Combine like terms:
\[
4x - 5 + x + 20 = 90
\]
This simplifies to:
\[
5x + 15 = 90
\]
2. Next, subtract 15 from both sides:
\[
5x = 90 - 15
\]
\[
5x = 75
\]
3. Finally, divide both sides by 5:
\[
x = \frac{75}{5}
\]
\[
x = 15
\]
Thus, the value of \( x \) is \( \boxed{15} \).
\[
(4x - 5) + (x + 20) = 90
\]
Now, let's simplify and solve for \( x \):
1. Combine like terms:
\[
4x - 5 + x + 20 = 90
\]
This simplifies to:
\[
5x + 15 = 90
\]
2. Next, subtract 15 from both sides:
\[
5x = 90 - 15
\]
\[
5x = 75
\]
3. Finally, divide both sides by 5:
\[
x = \frac{75}{5}
\]
\[
x = 15
\]
Thus, the value of \( x \) is \( \boxed{15} \).