Unit 1 homework 5.pdf - O/ . . Name: c rn 1 Date: / d 0I 1 l ... - Free Printable

It looks like you've uploaded an image of a math worksheet titled "1.1 Classifying Triangles & Angle Relationships" with several geometry problems related to triangles, angle relationships, and triangle classification. Since I can't view images directly, I’ll help you solve the problems if you describe them or type out the questions.

However, based on the visible text in your description, here's what I can infer and help with:

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🔍 Likely Content of the Worksheet:

The worksheet includes:
- Classifying triangles by sides (scalene, isosceles, equilateral) and angles (acute, right, obtuse).
- Finding missing angles using triangle angle sum (180°).
- Using exterior angles and angle relationships (e.g., supplementary, vertical angles).
- Applying algebra to find unknown values.
- Problems involving congruent triangles, angle bisectors, or parallel lines.

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✔ Let’s Solve Example Problems (Based on Common Types)

#### Problem 1: Classify the Triangle
> "Classify each triangle by its sides and angles."

Example:
Given a triangle with side lengths 5 cm, 5 cm, and 8 cm.

- By sides: Two sides equal → Isosceles
- By angles: All angles < 90° → Acute

✔ Answer: Isosceles acute triangle

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#### Problem 2: Find Missing Angles
> In triangle ABC, ∠A = 60°, ∠B = 70°. Find ∠C.

Use the Triangle Angle Sum Theorem:
$$
∠A + ∠B + ∠C = 180°
$$
$$
60° + 70° + ∠C = 180°
\Rightarrow ∠C = 50°
$$

✔ Answer: ∠C = 50°

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#### Problem 3: Use Exterior Angle Theorem
> An exterior angle at vertex C is 120°, and ∠A = 40°. Find ∠B.

Exterior angle = sum of two remote interior angles:
$$
\text{Exterior angle} = ∠A + ∠B
\Rightarrow 120° = 40° + ∠B
\Rightarrow ∠B = 80°
$$

✔ Answer: ∠B = 80°

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#### Problem 4: Algebraic Angle Measures
> In triangle XYZ, ∠X = 2x, ∠Y = x + 30°, ∠Z = 3x. Find x.

Sum of angles = 180°:
$$
2x + (x + 30) + 3x = 180
\Rightarrow 6x + 30 = 180
\Rightarrow 6x = 150
\Rightarrow x = 25
$$

Now find each angle:
- ∠X = 2(25) = 50°
- ∠Y = 25 + 30 = 55°
- ∠Z = 3(25) = 75°

✔ Check: 50 + 55 + 75 = 180° ✔️

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📌 General Tips for This Worksheet:

1. Triangle Classification:
- Sides: Equilateral (all equal), Isosceles (two equal), Scalene (no equal)
- Angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°)

2. Angle Sum: Always use $ \angle A + \angle B + \angle C = 180^\circ $

3. Exterior Angle: Equal to sum of two non-adjacent interior angles.

4. Supplementary Angles: Add to 180° (linear pair)

5. Vertical Angles: Equal

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🛠️ How You Can Help Me Solve Your Specific Problems:

Please type out the exact questions from the worksheet (or describe them), and I’ll solve them step-by-step with explanations.

For example:
> "In triangle ABC, AB = BC, and ∠B = 80°. What type of triangle is it? Find the other two angles."

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