Certainly! To find the complementary angles given as [tex]\(2x\)[/tex] and [tex]\(4x\)[/tex], let's follow these steps:
1. Understand the Definition of Complementary Angles:
Complementary angles are two angles whose measures add up to 90 degrees.
2. Set Up the Equation:
We know that the sum of [tex]\(2x\)[/tex] and [tex]\(4x\)[/tex] should be 90 degrees. Therefore, we can write the equation:
[tex]\[
2x + 4x = 90
\][/tex]
3. Combine Like Terms:
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
6x = 90
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Solve the equation by dividing both sides by 6:
[tex]\[
x = \frac{90}{6} = 15
\][/tex]
5. Calculate the Angles:
Now that we have the value of [tex]\(x\)[/tex], we can find the measures of the angles:
- For [tex]\(2x\)[/tex]:
[tex]\[
2x = 2 \times 15 = 30
\][/tex]
- For [tex]\(4x\)[/tex]:
[tex]\[
4x = 4 \times 15 = 60
\][/tex]
Therefore, the complementary angles are [tex]\(30\)[/tex] degrees and [tex]\(60\)[/tex] degrees.
