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Given that quadrilateral \( PQRS \) is a kite, we need to find the measure of angle \( \angle R \).

### Properties of a Kite:
1. A kite has two pairs of adjacent sides that are equal.
2. One pair of opposite angles (where the unequal sides meet) are congruent.

### Step-by-Step Solution:
1. From the diagram, we know:
   - \( m\angle S = 90^\circ \) (given).
   - \( m\angle Q = 74^\circ \) (given).
   
2. Since \( PQRS \) is a kite, the angles formed between the unequal sides are congruent. Therefore:
   - \( m\angle P = m\angle R \).

3. To find \( m\angle R \), we use the angle sum property of a quadrilateral, which states that the sum of the interior angles of a quadrilateral is \( 360^\circ \).

\[
m\angle S + m\angle Q + m\angle P + m\angle R = 360^\circ
\]

Substituting the known values:

\[
90^\circ + 74^\circ + m\angle R + m\angle R = 360^\circ
\]

Simplify the equation:

\[
164^\circ + 2m\angle R = 360^\circ
\]

\[
2m\angle R = 360^\circ - 164^\circ
\]

\[
2m\angle R = 196^\circ
\]

\[
m\angle R = 98^\circ
\]

### Final Answer:
\[
m\angle R = 98^\circ
\]

Would you like any more details or have any questions?

### Related Questions:
1. What are the properties of a kite in geometry?
2. How can you find the sum of the interior angles of a polygon?
3. What is the relationship between adjacent angles in a kite?
4. How do the properties of a kite differ from those of a parallelogram?
5. How do you calculate unknown angles in a quadrilateral?

### Tip:
Remember that the sum of the interior angles of any quadrilateral is always \( 360^\circ \), which is useful for solving unknown angles.

Quadrilateral PQRS is a kite. What is m∠R?

Learn how to calculate the measure of angle R in a kite-shaped quadrilateral PQRS, using properties of kites and the angle sum property of quadrilaterals. Suitable for students in Grades 8-10.

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