In `DeltaABC`, if `angleC = 50^(@) and angleA` exceeds `angleB` by `44^(@)`, then `angleA`

Options

A. `43^(@)`
B. `40^(@)`
C. `67^(@)`
D. `87^(@)`

Answer

To solve the problem, we need to find the measure of angle A in triangle ABC given that angle C = 50° and angle A exceeds angle B by 44°.

### Step-by-Step Solution:

1. **Define the Angles**:
Let angle B = x.
Since angle A exceeds angle B by 44°, we can express angle A as:
\[ \text{Angle A} = x + 44° \]

2. **Use the Triangle Sum Property**:
The sum of the angles in a triangle is always 180°. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
Substituting the known values:
\[ (x + 44°) + x + 50° = 180° \]

3. **Combine Like Terms**:
Simplifying the equation:
\[ 2x + 44° + 50° = 180° \]
\[ 2x + 94° = 180° \]

4. **Isolate the Variable**:
Subtract 94° from both sides:
\[ 2x = 180° - 94° \]
\[ 2x = 86° \]

5. **Solve for x**:
Divide both sides by 2:
\[ x = \frac{86°}{2} = 43° \]

6. **Find Angle A**:
Now substitute x back to find angle A:
\[ \text{Angle A} = x + 44° = 43° + 44° = 87° \]

### Final Answer:
Angle A = 87°.