To find the angles given that [tex]\(2x^\circ\)[/tex] and [tex]\((x + 15)^\circ\)[/tex] are complementary angles, we need to follow these steps:
1. Understand the Definition of Complementary Angles:
Complementary angles are two angles whose measures add up to [tex]\(90^\circ\)[/tex].
2. Set Up the Equation:
Since the angles are complementary, their sum should be equal to [tex]\(90^\circ\)[/tex]. Therefore, we can set up the equation as follows:
[tex]\[
2x + (x + 15) = 90
\][/tex]
3. Simplify the Equation:
Combine like terms in the equation:
[tex]\[
2x + x + 15 = 90
\][/tex]
[tex]\[
3x + 15 = 90
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
First, isolate [tex]\(3x\)[/tex] by subtracting [tex]\(15\)[/tex] from both sides of the equation:
[tex]\[
3x + 15 - 15 = 90 - 15
\][/tex]
[tex]\[
3x = 75
\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(3\)[/tex]:
[tex]\[
x = \frac{75}{3}
\][/tex]
[tex]\[
x = 25
\][/tex]
5. Find the Measures of Each Angle:
Now that we have [tex]\(x\)[/tex], we can find the measure of each angle.
- The measure of the first angle is [tex]\(2x\)[/tex]:
[tex]\[
2x = 2 \times 25 = 50^\circ
\][/tex]
- The measure of the second angle is [tex]\(x + 15\)[/tex]:
[tex]\[
x + 15 = 25 + 15 = 40^\circ
\][/tex]
6. Conclusion:
Therefore, the measures of the angles are [tex]\(50^\circ\)[/tex] and [tex]\(40^\circ\)[/tex].
Thus, the angles are [tex]\(50^\circ\)[/tex] and [tex]\(40^\circ\)[/tex].
