Question

Two complementary angles have measures (4x)°
and (2x)°
. What is the value of x
and the two angle measures?(2 points)
x=

, (4x)°=

°
, and (2x)°=

°
Remaining Attempts : 3

Answer 1

Complementary angles are two angles that add up to 90 degrees. Given the measures of the angles are \( (4x)^\circ \) and \( (2x)^\circ \), we can set up the following equation:

\[
4x + 2x = 90
\]

Combining like terms gives:

\[
6x = 90
\]

Now we can solve for \( x \):

\[
x = \frac{90}{6} = 15
\]

Now that we have found \( x \), we can find the measures of the two angles:

1. \( (4x)^\circ = 4 \cdot 15 = 60^\circ \)
2. \( (2x)^\circ = 2 \cdot 15 = 30^\circ \)

Thus, the values are:

- \( x = 15 \)
- \( (4x)^\circ = 60^\circ \)
- \( (2x)^\circ = 30^\circ \)

Final values:

\[
x = 15, \quad (4x)^\circ = 60^\circ, \quad (2x)^\circ = 30^\circ
\]