The measures of two angles of a quadrilateral are `70^(@)` and `90^(@)` and the other two angles are equal. Find the measure of each of the equal angles.

Answer

To solve the problem, we need to find the measures of the two equal angles in a quadrilateral where two angles are given as \(70^\circ\) and \(90^\circ\).

### Step-by-Step Solution:

1. **Understand the Sum of Angles in a Quadrilateral**:
The sum of the internal angles of a quadrilateral is always \(360^\circ\).

2. **Identify Given Angles**:
We are given:
- Angle A = \(70^\circ\)
- Angle B = \(90^\circ\)
- Let the two equal angles be Angle C and Angle D, both equal to \(x\).

3. **Set Up the Equation**:
According to the property of quadrilaterals, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]
Substituting the known values:
\[ 70^\circ + 90^\circ + x + x = 360^\circ \]

4. **Combine Like Terms**:
Combine the known angles:
\[ 160^\circ + 2x = 360^\circ \]

5. **Isolate the Variable**:
To find \(x\), first subtract \(160^\circ\) from both sides:
\[ 2x = 360^\circ - 160^\circ \]
\[ 2x = 200^\circ \]

6. **Solve for \(x\)**:
Divide both sides by 2:
\[ x = \frac{200^\circ}{2} = 100^\circ \]

7. **Conclusion**:
Therefore, the measure of each of the equal angles (Angle C and Angle D) is \(100^\circ\).

### Final Answer:
Each of the equal angles is \(100^\circ\).

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