`angleA` and `angleB` are complementary angles. If `angleA=x+20^(@)` and `angleB=x-10^(@)`, find `angleA` and `angleB`.

Answer

To solve the problem, we need to find the measures of angle A and angle B, given that they are complementary angles. Here are the steps to solve the question:

### Step 1: Understand the definition of complementary angles.
Complementary angles are two angles whose sum is 90 degrees.

### Step 2: Write down the expressions for angle A and angle B.
We are given:
- Angle A = x + 20°
- Angle B = x - 10°

### Step 3: Set up the equation based on the property of complementary angles.
Since angle A and angle B are complementary, we can write the equation:
\[ \text{Angle A} + \text{Angle B} = 90° \]
Substituting the expressions for angle A and angle B:
\[ (x + 20°) + (x - 10°) = 90° \]

### Step 4: Simplify the equation.
Combine like terms:
\[ x + x + 20° - 10° = 90° \]
This simplifies to:
\[ 2x + 10° = 90° \]

### Step 5: Solve for x.
To isolate x, subtract 10° from both sides:
\[ 2x = 90° - 10° \]
\[ 2x = 80° \]
Now, divide both sides by 2:
\[ x = \frac{80°}{2} \]
\[ x = 40° \]

### Step 6: Find the measure of angle A.
Now that we have the value of x, we can find angle A:
\[ \text{Angle A} = x + 20° = 40° + 20° = 60° \]

### Step 7: Find the measure of angle B.
Now, we can find angle B:
\[ \text{Angle B} = x - 10° = 40° - 10° = 30° \]

### Step 8: Conclusion.
Thus, the measures of angle A and angle B are:
- Angle A = 60°
- Angle B = 30°

### Verification:
To verify, we can check if the sum of angle A and angle B equals 90°:
\[ 60° + 30° = 90° \]
This confirms that our solution is correct.

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