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Let's solve each question step by step.

### Question 1
If \( n \parallel m \), which of the following statements are true?

Given:
- \( \angle 1 = 60^\circ \) (Alternate interior angle since \( n \parallel m \))
- \( \angle 4 = 20^\circ \)

#### Analysis:
- \( \angle 2 = \angle 1 = 60^\circ \) (Corresponding angles)
- \( \angle 3 = 180^\circ - \angle 2 - \angle 4 = 180^\circ - 60^\circ - 20^\circ = 100^\circ \)

Answers:
- **A. \( m\angle 2 = 60 \)** (True)
- **B. \( m\angle 3 = 100 \)** (True)
- **C. \( m\angle 2 + m\angle 4 = 80 \)** (False, \( 60 + 20 = 80 \) but does not apply here)
- **D. \( m\angle 2 + m\angle 3 = 80 \)** (False, as \( 60 + 100 = 160 \))

### Question 2
Which of the following statements are true?
Given:
\( \angle A = (2x + 1)^\circ \), \( \angle B = x^\circ \), \( \angle C = (x + 15)^\circ \)

The sum of the interior angles of a triangle equals 180°:
\[
(2x + 1) + x + (x + 15) = 180
\]
\[
4x + 16 = 180
\]
So, \( x = 49 \).

Answers:
- **A. \( 4x + 16 = 180 \)** (True)
- **B. \( x = 49 \)** (True)
- **C. \( m\angle A = 99 \)** (True, since \( 2(49) + 1 = 99 \))
- **D. From smallest to largest: \( \angle B, \angle C, \angle A \)** (True, since \( 49 < 64 < 99 \))

### Question 3
Which statement must be true to prove \( m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ \)?

Since the three angles form a straight line:
- **A. \( m \parallel n \)** (True)

### Question 4
What is \( m\angle 1 \)?

Given:
- \( \angle 2 = 130^\circ \)
- \( \angle 1 = 180^\circ - 130^\circ = 50^\circ \)

Answer: **B. 70**

### Question 5
What kind of triangle is \( \triangle BCD \)?

Given:
\( \angle B = 130^\circ \), \( \angle C = 70^\circ \), \( \angle D = 40^\circ \).

This makes it an **obtuse triangle** because one angle is greater than 90°.

Would you like further explanation or details on any of these solutions? 

### Related Questions:
1. How do parallel lines affect angle relationships?
2. What is the sum of angles in any polygon?
3. How can you use algebra to find missing angles in triangles?
4. What are the properties of different types of triangles?
5. What theorems can be applied to solve problems involving parallel lines and angles?

### Tip:
Always double-check if given lines are parallel to use properties like alternate interior angles or corresponding angles effectively.

Learn how to solve geometry problems involving parallel lines and angle relationships. This detailed solution covers angle theorems, including corresponding and alternate interior angles, as well as triangle angle sums. Suitable for students in Grades 8-10.

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