if two angles are supplementary. one angle is twice the other. what are the 2 angles? Show all work. 

When two angles are supplementary, their sum is always \(180^\circ\). Given that one angle is twice the other, we can set up the problem as follows:

### Step 1: Define the angles
Let the smaller angle be \(x\). Then, the other angle, which is twice the smaller one, is \(2x\).

### Step 2: Set up the equation
Since the angles are supplementary, their sum is \(180^\circ\):
\[
x + 2x = 180^\circ
\]

### Step 3: Solve the equation
Combine like terms:
\[
3x = 180^\circ
\]

Now, solve for \(x\) by dividing both sides by 3:
\[
x = \frac{180^\circ}{3} = 60^\circ
\]

### Step 4: Find the second angle
Since the second angle is twice the smaller one:
\[
2x = 2(60^\circ) = 120^\circ
\]

### Step 5: Conclusion
The two angles are \(60^\circ\) and \(120^\circ\).

### Check
\[
60^\circ + 120^\circ = 180^\circ
\]
This confirms that the angles are supplementary.

Would you like further clarification or more details on this problem?

Here are 5 related questions you can explore:
1. What are complementary angles and how do they differ from supplementary angles?
2. If the sum of two angles is 90°, how can we find them if one angle is twice the other?
3. How can we determine the angles if the ratio between them is 3:5 and they are supplementary?
4. How do we solve for angles in polygons if the sum of interior angles is known?
5. Can supplementary angles be non-adjacent? How would that affect their properties?

**Tip:** When solving angle problems, always write down the relationships between the angles clearly before solving the equation.

If two angles are supplementary, one angle is twice the other. What are the two angles? Show all work.

Learn how to find two supplementary angles when one angle is twice the other with this step-by-step solution. This problem covers key concepts like supplementary angles and algebraic equations, suitable for students in Grades 6-8.

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