https://file.aiquickdraw.com/mathbot/file/17309353704818fncr3u1.jpg

Let's solve the questions one by one based on the image you've provided.

### Question 17 & 18
From the figure provided:
1. **m∠1 = 125°**
2. **m∠2 = 90°** (since it's a right angle marked by a 90° symbol)

### Question 19
For this problem:
- We are given two remote interior angles of a triangle: **37°** and **62°**.
- The sum of all interior angles of a triangle is 180°.

1. Calculate the third angle of the triangle:
   \[
   180° - (37° + 62°) = 180° - 99° = 81°
   \]

2. The exterior angle associated with the two remote interior angles (37° and 62°) is the sum of those angles:
   \[
   37° + 62° = 99°
   \]

   Therefore:
   - The measure of the third angle is **81°**.
   - The measure of the exterior angle associated with the two remote interior angles is **99°**.

### Questions 20, 21, 22, and 23 (based on the second figure)
In this figure:
- **∠A = (2x + 2)°**
- **∠C = (x + 4)°**
- **∠B** is given as **x°**.

Since it's a triangle, the sum of the angles in a triangle should be **180°**.

#### Step 1: Set up the equation for the triangle
\[
(2x + 2) + (x + 4) + x = 180
\]

#### Step 2: Simplify and solve for \(x\)
\[
4x + 6 = 180
\]
\[
4x = 174
\]
\[
x = 43.5
\]

#### Step 3: Substitute \(x = 43.5\) into each angle expression
1. **m∠A = (2x + 2)**:
   \[
   2(43.5) + 2 = 87 + 2 = 89°
   \]

2. **m∠C = (x + 4)**:
   \[
   43.5 + 4 = 47.5°
   \]

3. **m∠B = x**:
   \[
   43.5°
   \]

#### Answers:
- **m∠A = 89°**
- **m∠C = 47.5°**
- **m∠ABC = m∠B = 43.5°**
- **m∠ABD = 43.5°** (since ∠ABD is essentially ∠B here in this configuration)

Would you like a more detailed explanation of any specific step, or do you have any further questions?

### Follow-up Questions:
1. How would you calculate an exterior angle in a triangle if only two interior angles are known?
2. What is the importance of understanding the properties of angles in a triangle?
3. Can you explain how the sum of the interior angles in a triangle can help solve for unknown variables?
4. How would these angle relationships change if the shape were not a triangle?
5. Why is it necessary to verify that the sum of all angles equals 180° in triangle problems?

### Tip:
Remember that in any triangle, knowing two angles always allows you to find the third, as their sum must equal 180°.

Solve the angles and measurements in the provided triangle problems, including finding the measure of missing angles based on given expressions and properties of triangles.

This guide provides a step-by-step solution for finding unknown angles in triangles using properties like the triangle angle sum theorem and exterior angle theorem. Includes worked examples and algebraic methods suitable for students in Grades 7-9.

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