Whats the Angle? | Worksheet - Free Printable

Let’s go step by step through each part of the worksheet.

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Part 1: Choose the best estimate for the measure of each angle.

We are given two angles and four choices for each.

First angle (left):
It looks like an obtuse angle — bigger than 90°, but not too big. The options are:
a) 80° → too small (acute)
b) 29° → way too small
c) 75° → still acute, less than 90°
d) 76° → also acute

Wait — none of these look right? Let me check again.

Actually, looking at the diagram:
The first angle is drawn with one ray going left-down and the other going up-right — it’s clearly obtuse, meaning >90°. But all the answer choices are under 90°? That can’t be.

Hold on — maybe I misread. Let me re-express:

Looking carefully at the first angle in Part 1:
Vertex at B, rays BA and BC. Ray BA goes down-left, ray BC goes right. So the angle opens upward — actually, it might be acute? Wait no — if you trace from BA to BC, turning counterclockwise, it’s more than 90°? Hmm.

But let’s compare visually to known angles:

- A right angle is 90° (like corner of paper).
- This angle looks a bit larger than that? Or smaller?

Actually, looking again — perhaps it's meant to be estimated as about 80°? Because it’s close to 90° but slightly less? But the drawing shows it opening wider...

Wait — maybe there’s a trick. Let’s look at the second angle in Part 1.

Second angle (right):
Vertex at X, rays XY and XZ. Ray XY goes down-left, ray XZ goes right. The angle between them — this one looks very narrow, definitely acute, probably around 20–30°.

Options for second angle:
a) 29°
b) 79°
c) 60°
d) 10°

So 29° or 10°? It doesn’t look as tiny as 10° — more like 25–30°. So 29° is reasonable.

Now back to first angle: If the second is ~29°, then the first must be the larger one among its options. Its options: 80°, 29°, 75°, 76° — so 80° is largest. And visually, the first angle does look closer to 80° than 75° or 76°? Actually, 80° is very close to 90° — and the angle drawn does look almost like a right angle but slightly open — so yes, 80° is best estimate.

But wait — let me double-check standard estimation:

In many textbooks, when they show an angle that looks “almost straight” but bent a little, it’s often 80° or 100°. Since 100° isn’t an option, and 80° is, and it’s the only one near 90°, we’ll go with 80°.

So:

First angle → a) 80°
Second angle → a) 29°

Wait — hold on! For the second angle, option a is 29°, which matches our guess. But let’s confirm: Is there any chance it’s 10°? No — 10° would be extremely sharp, like a needle point. This has some width — so 29° is correct.

✔ Part 1 Answers:
Left angle: 80°
Right angle: 29°

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Part 2: Find the angle measure for each problem.

These give us diagrams with some angles labeled, and we need to find missing ones using geometry rules.

Problem 1: m∠ABC = ?

Diagram: Points A-B-C, with D above B. Angle ABD is marked 45°, angle DBC is marked 25°. So ∠ABC is made of those two parts: 45° + 25° = 70°

✔ m∠ABC = 70°

Problem 2: m∠FEG = ?

Diagram: Point E, with rays EF, EG, EH. Angle FEH is 98°, angle HEG is 44°. We want angle FEG — which is the whole angle from F to G passing through H? Or directly?

Looking at the arc: The pink arc goes from F to G, skipping H? Wait — actually, the diagram likely shows that ∠FEH = 98°, and ∠HEG = 44°, and points F-E-H-G are arranged such that H is between F and G? Then ∠FEG = ∠FEH + ∠HEG = 98° + 44° = 142°

But wait — sometimes the arc indicates the reflex angle? No, in basic geometry problems like this, unless specified, we take the smaller angle. But 98+44=142, which is less than 180, so it’s fine.

Alternatively, maybe H is inside angle FEG? Yes — so adding makes sense.

✔ m∠FEG = 142°

Problem 3: m∠KLM = ?

Diagram: Points K-L-M, with N above L. Angle KLN is 58°, angle NLM is 27°. So KLM = 58° + 27° = 85°

✔ m∠KLM = 85°

Problem 4: m∠ZYX = ?

Diagram: Points Z-Y-X, with W above Y. Angle WYZ is 33°, angle WYX is 57°. We want ∠ZYX — which is the angle from Z to X via Y.

If W is between Z and X, then ∠ZYX = ∠WYZ + ∠WYX = 33° + 57° = 90°

That makes sense — and 90° is a nice number, often used in problems.

✔ m∠ZYX = 90°

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Part 3: Use the image to help you answer the following questions.

Diagram: Line AC horizontal, point B on it. Line EB vertical upward from B. Line DB going up-right from B, making angle CBD = 35°. Also, angle EBD is marked with a square? Wait — no, in the description, it says “Name a right angle”, etc.

From the setup:

- AC is a straight line → 180°
- EB is perpendicular to AC? Probably, since it’s drawn vertically and AC horizontally — so ∠EBA and ∠EBC should be 90° each.

Also, angle CBD = 35° — that’s between CB and DB.

Question 1: Name a right angle.

A right angle is 90°. From the diagram, since EB AC, then:

→ ∠EBA = 90°
→ ∠EBC = 90°

Either is acceptable. Let’s pick ∠EBC (since C is on the right, and B is vertex).

Question 2: What is the measure of ∠EBD?

Point D is between E and C? Looking at positions:

From B:
- Left: A
- Right: C
- Up: E
- Up-right: D, with CBD = 35°

Since ∠EBC = 90° (right angle), and CBD = 35°, then ∠EBD = ∠EBC - ∠CBD = 90° - 35° = 55°

Because D is between E and C, so subtracting gives the angle between E and D.

✔ ∠EBD = 55°

Question 3: What is the measure of ∠ABD?

ABD is from A to D via B.

We know:

- ∠ABC = 180° (straight line)
- ∠CBD = 35°
- So ∠ABD = ∠ABC - ∠CBD = 180° - 35° = 145°

Alternatively: ∠ABE = 90°, ∠EBD = 55°, so ∠ABD = 90° + 55° = 145° — same result.

✔ ABD = 145°

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Now, compiling all answers:

Part 1:
Left angle: 80° → choice a
Right angle: 29° → choice a

Part 2:
m∠ABC = 70°
m∠FEG = 142°
m∠KLM = 85°
m∠ZYX = 90°

Part 3:
1. Right angle: ∠EBC (or ∠EBA)
2. m∠EBD = 55°
3. m∠ABD = 145°

Final Answer:

Part 1:
Left angle: a) 80°
Right angle: a) 29°

Part 2:
m∠ABC = 70°
m∠FEG = 142°
m∠KLM = 85°
m∠ZYX = 90°

Part 3:
1. EBC (or ∠EBA)
2. 55°
3. 145°