The larger of two supplementary angles exceeds thrice the smaller by 20 degrees. Find them.

Answer

To solve the problem of finding two supplementary angles where the larger angle exceeds thrice the smaller angle by 20 degrees, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( L \) = the larger angle
- \( S \) = the smaller angle

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The angles are supplementary, which means:
\[ L + S = 180 \quad \text{(Equation 1)} \]
2. The larger angle exceeds thrice the smaller angle by 20 degrees:
\[ L = 3S + 20 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
We can substitute the expression for \( L \) from Equation 2 into Equation 1:
\[ (3S + 20) + S = 180 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 4S + 20 = 180 \]

### Step 5: Solve for \( S \)
Subtract 20 from both sides:
\[ 4S = 160 \]
Now, divide by 4:
\[ S = 40 \]

### Step 6: Find \( L \)
Now that we have \( S \), we can find \( L \) using Equation 2:
\[ L = 3(40) + 20 \]
\[ L = 120 + 20 = 140 \]

### Step 7: Conclusion
The larger angle \( L \) is 140 degrees, and the smaller angle \( S \) is 40 degrees.

### Final Answer
- Larger angle \( L = 140^\circ \)
- Smaller angle \( S = 40^\circ \)

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