Question
Two complementary angles have measures (4x)°
and (2x)°
. What is the value of x
and the two angle measures?
and (2x)°
. What is the value of x
and the two angle measures?
Answers
GPT-4o mini
Complementary angles are two angles that add up to 90 degrees. Given the two angles are \( (4x)^\circ \) and \( (2x)^\circ \), we can set up the following equation:
\[
4x + 2x = 90
\]
Combining like terms:
\[
6x = 90
\]
Now, we can solve for \( x \) by dividing both sides by 6:
\[
x = \frac{90}{6} = 15
\]
Now that we have the value of \( x \), we can find the measures of the two angles:
1. The first angle:
\[
4x = 4(15) = 60^\circ
\]
2. The second angle:
\[
2x = 2(15) = 30^\circ
\]
Thus, the value of \( x \) is \( 15 \), and the measures of the two angles are \( 60^\circ \) and \( 30^\circ \).
\[
4x + 2x = 90
\]
Combining like terms:
\[
6x = 90
\]
Now, we can solve for \( x \) by dividing both sides by 6:
\[
x = \frac{90}{6} = 15
\]
Now that we have the value of \( x \), we can find the measures of the two angles:
1. The first angle:
\[
4x = 4(15) = 60^\circ
\]
2. The second angle:
\[
2x = 2(15) = 30^\circ
\]
Thus, the value of \( x \) is \( 15 \), and the measures of the two angles are \( 60^\circ \) and \( 30^\circ \).