In the adjoining figure PQ = PR and ` angle PRQ = 70^(@) ` Find ` angle QPR. `

Answer

To solve the problem step by step, we will use the properties of triangles and the information given in the question.

### Step-by-Step Solution:

1. **Identify the Triangle**: We have triangle PQR where PQ = PR and angle PRQ = 70°.

2. **Use the Property of Isosceles Triangles**: Since PQ = PR, triangle PQR is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, angle PQR = angle PRQ.

\[ \text{Let } \angle PQR = x. \]
Since PQ = PR, we have:
\[ x = \angle PRQ = 70°. \]

3. **Calculate the Angles in the Triangle**: Now we know that:
\[ \angle PQR = 70°. \]
We also denote angle QPR as \( y \).

4. **Apply the Angle Sum Property of Triangles**: The sum of the angles in a triangle is always 180°. Therefore, we can write:
\[ \angle PQR + \angle PRQ + \angle QPR = 180°. \]
Substituting the known values:
\[ 70° + 70° + y = 180°. \]

5. **Solve for angle QPR**:
\[ 140° + y = 180°. \]
To find \( y \), subtract 140° from both sides:
\[ y = 180° - 140° = 40°. \]

6. **Conclusion**: Therefore, the measure of angle QPR is:
\[ \angle QPR = 40°. \]

### Final Answer:
\[ \angle QPR = 40°. \]