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We are given a triangle \( \triangle BCD \) with the following information:

- \( \angle C = 70^\circ \)
- \( \angle D = 130^\circ \)

We need to find the measure of \( \angle 1 \), which is denoted as \( m \angle 1 \).

### Step-by-step solution:

1. **Exterior Angle Theorem**: 
   The angle \( \angle D \) is an exterior angle of triangle \( BCD \), and the Exterior Angle Theorem tells us that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

2. In this case:
   \[
   \angle D = \angle 1 + \angle C
   \]
   Substituting the known values:
   \[
   130^\circ = \angle 1 + 70^\circ
   \]

3. Solving for \( \angle 1 \):
   \[
   \angle 1 = 130^\circ - 70^\circ = 60^\circ
   \]

### Final Answer:
The measure of \( \angle 1 \) is \( 60^\circ \), so the correct choice is **A**.

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Would you like more details or have any questions?

Here are 5 related questions:
1. How does the exterior angle theorem apply to any triangle?
2. Can you use the interior angles of the triangle to verify this result?
3. What is the sum of the interior angles in any triangle?
4. How do you calculate an unknown angle in a triangle if two angles are given?
5. What happens if the exterior angle is obtuse or acute?

**Tip**: Always remember the exterior angle theorem—it’s a quick way to solve many geometry problems involving triangles!

Learn how to solve for an unknown angle in a triangle using the Exterior Angle Theorem. In this problem, given angles 70° and 130°, we calculate the missing angle (m∠1) in triangle BCD. Suitable for students in Grades 6-8.

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