Two angles of a quadrilateral measure `85^(@) and 75^(@)` respectively. The other two angles are equal. Find the measure of each of these equal angles.

Options

A. `110^(@)`
B. `102^(@)`
C. `100^(@)`
D. `120^(@)`

Answer

To solve the problem, we need to find the measure of the two equal angles in the quadrilateral given that two angles measure 85 degrees and 75 degrees.

### Step-by-Step Solution:

1. **Understand the properties of a quadrilateral**: The sum of all interior angles in a quadrilateral is always 360 degrees.

2. **Identify the known angles**: We have two angles given:
- Angle 1 = 85 degrees
- Angle 2 = 75 degrees

3. **Calculate the sum of the known angles**:
\[ \text{Sum of known angles} = 85 + 75 = 160 \text{ degrees} \]

4. **Determine the sum of the unknown angles**: Since the total sum of angles in a quadrilateral is 360 degrees, we can find the sum of the two equal angles (let's call them \( x \)):
\[ \text{Sum of unknown angles} = 360 - 160 = 200 \text{ degrees} \]

5. **Set up the equation for the equal angles**: Since both unknown angles are equal, we can express this as:
\[ 2x = 200 \]

6. **Solve for \( x \)**:
\[ x = \frac{200}{2} = 100 \text{ degrees} \]

7. **Conclusion**: Each of the equal angles measures 100 degrees.

### Final Answer:
The measure of each of the equal angles is **100 degrees**.