Working With Congruent Angles | 8th Grade Geometry Worksheets - Free Printable

Let’s work through this step by step.

The worksheet has two parts:

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Part 1: Circle the congruent angle for each angle below.

Congruent angles are angles that have the same measure — they look identical in shape and size, even if rotated or flipped.

We’ll go one by one:

1) The given angle is a right angle (looks like an “L” shape).
→ Look at options:
A) Acute angle (less than 90°) — no
B) Straight angle (180°) — no
C) Right angle — YES! Same as original.
✔ Answer: C

2) Given angle is acute, pointing down-left.
→ Options:
A) Acute, but wider — probably not same measure
B) Obtuse — too big
C) Very narrow acute — might be same? Let’s compare carefully. Actually, looking closely, option A matches the opening size best. But wait — let’s think visually. Original is about 45°, Option A looks similar. Option C is sharper. So likely A.
But hold on — actually, in many worksheets like this, they expect exact visual match. Rechecking:
Original: ~60°?
Option A: ~60° — yes
Option B: >90° — no
Option C: <45° — no
✔ Answer: A

Wait — I need to be more precise. Since we can’t measure with protractor here, we rely on visual matching. In standard worksheets, these are designed so only one matches exactly.

Actually, let me re-evaluate all using logic:

For #2: The angle opens downward-left. Option A opens upward-right — same shape, just mirrored — still congruent! Congruent doesn’t care about direction. So if it looks same width, it’s congruent.

Looking again:
- Original: medium acute
- A: medium acute — matches
- B: obtuse — no
- C: very sharp — no
✔ So A is correct.

3) Given angle is obtuse, open to left.
→ Options:
A) Acute — no
B) Right angle — no
C) Obtuse, open to right — same size? Visually yes — just flipped. Congruent!
✔ Answer: C

4) Given angle is reflex? No — wait, it’s less than 180°, looks like ~120°, open to right.
→ Options:
A) Smaller acute — no
B) Similar obtuse, open to left — same size? Yes — mirror image → congruent
C) Right angle — no
✔ Answer: B

So Part 1 answers:
1) C
2) A
3) C
4) B

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Part 2: Draw a congruent angle for each angle below.

This part asks you to draw — since we’re text-based, I’ll describe what to draw.

You must copy the exact angle measure and shape.

A) 60° — Draw an acute angle that looks like an equilateral triangle corner. Use ruler and protractor if allowed. Make sure both rays are same length as original for neatness.

B) 120° — This is obtuse. Imagine a clock from 12 to 4 — that’s 120°. Open wider than 90°, less than 180°.

C) 30° — Very narrow acute angle. Like half of 60°. Think of slicing pizza into 12 pieces — each slice is 30°.

D) 200° — Wait — 200° is greater than 180° — that’s a reflex angle! It goes past straight line. To draw: start with one ray going right, then rotate counterclockwise more than halfway around — stops at 200°, which is 20° past 180°. Or clockwise 160° — either way, total turn is 200°.

Note: Sometimes students confuse 200° with 160° — remember: 180° is straight line, so 200° bends back slightly beyond that.

Since we can’t draw here, student should use protractor to replicate each exactly.

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Final Answers Summary:

Part 1:
1) C
2) A
3) C
4) B

Part 2: Student draws copies of 60°, 120°, 30°, and 200° angles accurately.

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Final Answer:
Part 1: 1) C, 2) A, 3) C, 4) B
Part 2: Draw accurate copies of 60°, 120°, 30°, and 200° angles using protractor.