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If [tex]2x[/tex] and [tex]4x[/tex] are complementary angles, find their measures.

Sagot :

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.