Angles Revision Worksheet: Practice naming angles and calculating missing angles using geometric principles.

Let’s work through each part step by step.

---

Part 1: Name the angles below.

We look at each angle and match it to its type:

- A: This is more than 90° but less than 180° → Obtuse angle
- B: Has a square corner → exactly 90° → Right angle
- C: Less than 90° → Acute angle
- D: More than 90° but less than 180° → Obtuse angle

Wait — let’s double-check D. It looks like it could be reflex? No, the arc shown is inside the angle, and it’s clearly greater than 90° but not over 180°. So yes, obtuse.

Actually, looking again — in diagram A, the arc goes around the *outside*, meaning it’s showing the larger angle — which would be reflex (greater than 180°). That changes things!

So re-evaluating:

- A: The arc shows the big angle going the long way → Reflex angle
- B: Square symbol → Right angle
- C: Small sharp angle → Acute angle
- D: Looks like it’s between 90° and 180° → Obtuse angle

Yes, that makes sense with standard notation.

---

Part 2: Find missing angles.

(a) Angles on a straight line add to 180°.
Given: 22° + a = 180°
→ a = 180 - 22 = 158°

(b) Two angles make a right angle (90°), since there’s a square corner.
Given: b + 38° = 90°
→ b = 90 - 38 = 52°

(c) Three angles meet at a point on one side of a line? Wait — actually, they’re all meeting at a point, and together they form a straight line? Let’s see: 51°, c, and a right angle (90°) are adjacent along a straight line? Actually, no — looking at the diagram, it seems like three angles around a point on one side of a vertical line? Hmm.

Actually, better approach: The three angles (51°, c, and 90°) lie on a straight line? No — wait, the diagram shows them forming half a circle? Actually, no — if you look closely, the 51°, c, and 90° are all next to each other and their outer edges form a straight line. So total should be 180°.

So: 51 + c + 90 = 180
→ c = 180 - 51 - 90 = 39°

(d) Three angles on a straight line: 65°, 52°, d
Sum = 180°
→ d = 180 - 65 - 52 = 63°

(e) Two lines crossing → vertically opposite angles are equal. Also, angles on a straight line add to 180°.

We’re given one angle as 130°. Then e is vertically opposite to 130°? Wait — no, e is adjacent to 130° on a straight line.

Actually, looking: e and 130° are on a straight line → e + 130 = 180 → e = 50°

Then f is vertically opposite to e → so f = e = 50°? But wait — that can’t be because then the other two angles would also need to add up.

Wait — better: When two lines cross, four angles are formed. Opposite angles are equal. Adjacent angles add to 180°.

If one angle is 130°, then the angle opposite to it is also 130°. The other two angles (which are opposite each other) must each be 180 - 130 = 50°.

In the diagram, e and f are labeled near the top-left and top-right. If 130° is bottom, then e and f are likely the two 50° angles? But the diagram labels e and f separately — probably e is one 50°, f is the other 50°? Or maybe f is the opposite of 130°?

Wait — let me think differently. In diagram (e), we have an X shape. One angle is marked 130° at the bottom. Then e is top-left, f is top-right. Since vertically opposite angles are equal, the angle opposite 130° is also 130° — that would be the top one? But both e and f are at the top? That doesn’t make sense.

Actually, looking again — perhaps e and f are the two angles adjacent to the 130°? No — typically in such diagrams, when they label e and f like that, e might be adjacent to 130°, and f might be vertically opposite.

But to avoid confusion — let’s use the rule: angles around a point sum to 360°, but here it’s two intersecting lines, so we can use straight lines.

Assume the 130° is one angle. Then the angle next to it on the same straight line is 180 - 130 = 50°. That 50° is vertically opposite to another 50°, and the remaining two angles are both 130°.

In the diagram, if 130° is at the bottom, then the top angle is also 130° (vertically opposite). The left and right angles are both 50°.

Now, where are e and f placed? Typically, e might be the left angle, f the right — or vice versa. But since they’re symmetric, both should be 50°? But the problem asks for e= and f= separately — implying they might be different.

Wait — perhaps f is the vertically opposite angle to 130°? Then f = 130°, and e is adjacent, so e = 50°.

That makes sense. Let’s go with that.

So:
- e is adjacent to 130° on a straight line → e = 180 - 130 = 50°
- f is vertically opposite to 130° → f = 130°

Yes, that fits.

(f) Four angles around a point: 140°, 145°, g, and another angle? Wait — only three are labeled? No — looking: 140°, 145°, and g — but that’s only three. There must be a fourth.

Actually, in diagram (f), it’s three lines meeting at a point, creating four angles. We’re given 140°, 145°, and g — but g is one of them. The fourth angle isn’t labeled, but we know all four add to 360°.

So: 140 + 145 + g + ? = 360 — but we don’t know the fourth.

Wait — perhaps the 140° and 145° are adjacent, and g is opposite something? Better: list all knowns.

Actually, looking carefully: the diagram shows three rays from a point, dividing the space into three angles? No — three lines usually create six angles, but here it’s drawn as three sectors.

Perhaps it’s simpler: the angles around the point are 140°, 145°, and g — but that sums to more than 360 already? 140+145=285, so g would be 75? But that leaves no room for the fourth angle.

I think I miscounted. In diagram (f), there are four angles around the point. Labeled: 140°, 145°, g, and one unlabeled. But the unlabeled one is between 140° and 145°? No.

Actually, standard interpretation: when three lines meet at a point, they form six angles, but often we consider the three pairs of vertically opposite angles.

But in this case, the diagram likely shows four distinct angles adding to 360°. Given: 140°, 145°, and g — and the fourth is implied to be found.

But 140 + 145 = 285, so the remaining two angles sum to 75°. But we have only g labeled — so perhaps g is one of them, and the other is not needed? That doesn’t help.

Wait — perhaps the 140° and 145° are adjacent, and g is the angle opposite the combination? I’m overcomplicating.

Let me assume that the four angles are: A=140°, B=145°, C=g, D=?. And A+B+C+D=360°.

But without more info, we can’t find g alone. Unless... perhaps g is vertically opposite to something.

Another idea: maybe the 140° and 145° are on one side, and g is on the other, but still.

Looking back at the image description — in many such worksheets, for diagram (f), it's common that the angles are arranged such that 140° and 145° are adjacent, and g is the angle between them or something.

Perhaps it's a typo in my reasoning. Let me calculate what g must be if we assume the fourth angle is x, but we don't know x.

Wait — I recall that in some diagrams, when they show three angles around a point with one missing, and the others given, but here three are given including g.

Perhaps the 140° and 145° are not both full angles; maybe they overlap.

I think I need to reinterpret. Let's say the point has four regions. The angles are: between ray1 and ray2: 140°, between ray2 and ray3: 145°, between ray3 and ray4: g, and between ray4 and ray1: ?. Sum to 360°.

Still stuck.

Alternative approach: perhaps the 140° and 145° are vertically opposite or something. But 140 ≠ 145, so not.

Another thought: maybe "g" is the angle that completes the circle with 140° and 145°, but that would require knowing how many angles.

Let's count the number of angles shown. In diagram (f), it's likely three angles are labeled: 140°, 145°, and g, and they are consecutive, so their sum plus the fourth equals 360. But we have three unknowns effectively.

Unless... perhaps the fourth angle is zero, which is impossible.

I think I made a mistake earlier. Let me search for a different strategy.

Upon second thought, in many textbook problems, for a figure like (f), it's often that the angles are 140°, 145°, and g, and they are the only three, but that can't be since 140+145+g = 360 implies g=75, but then why label only three? Perhaps it's correct.

140 + 145 = 285, 360 - 285 = 75, so g = 75°.

And the fourth angle is not labeled, but in the diagram, it might be included in the labeling or assumed.

Perhaps g is the reflex angle or something, but unlikely.

I'll go with g = 360 - 140 - 145 = 75°, assuming those are three of the four angles, and the fourth is not needed for g.

But that seems arbitrary. Let's see the answer later.

For now, tentatively g = 75°.

(g) Angles on a straight line: h + 38° + 73° = 180°
→ h = 180 - 38 - 73 = 69°

(h) Angles around a point: 78° + 85° + 130° + i = 360°
Sum of knowns: 78 + 85 = 163; 163 + 130 = 293
→ i = 360 - 293 = 67°

(i) Angles around a point: 82° + j + 73° + 90° (since there's a right angle symbol) = 360°
Sum of knowns: 82 + 73 = 155; 155 + 90 = 245
→ j = 360 - 245 = 115°

Now back to (f): let's confirm.

In diagram (f), if we have four angles: let's call them A=140°, B=145°, C=g, D=x. A+B+C+D=360.

But we have only three labeled. Perhaps g is not one of the small angles; maybe it's the large one.

Another possibility: the 140° and 145° are adjacent, and g is the angle between the other two rays, but still.

Perhaps the diagram shows that 140° and 145° are on one side, and g is on the other, but with three lines, it's messy.

I recall that in some versions, for (f), the angles are 140°, 145°, and the third is g, and they add to 360, so g=75°. I think that's intended.

So g = 360 - 140 - 145 = 75°.

Yes.

Now summarize all answers:

Part 1:
A: Reflex angle
B: Right angle
C: Acute angle
D: Obtuse angle

Part 2:
(a) a = 158°
(b) b = 52°
(c) c = 39°
(d) d = 63°
(e) e = 50°, f = 130°
(f) g = 75°
(g) h = 69°
(h) i = 67°
(i) j = 115°

Double-check calculations:

(a) 180 - 22 = 158 ✓
(b) 90 - 38 = 52 ✓
(c) 51 + 90 = 141; 180 - 141 = 39 ✓
(d) 65 + 52 = 117; 180 - 117 = 63 ✓
(e) e = 180 - 130 = 50; f = 130 (vertical) ✓
(f) 140 + 145 = 285; 360 - 285 = 75 ✓
(g) 38 + 73 = 111; 180 - 111 = 69 ✓
(h) 78 + 85 = 163; 163 + 130 = 293; 360 - 293 = 67 ✓
(i) 82 + 73 = 155; 155 + 90 = 245; 360 - 245 = 115 ✓

All good.

Final Answer:

1. A: Reflex angle, B: Right angle, C: Acute angle, D: Obtuse angle
2. (a) a = 158°, (b) b = 52°, (c) c = 39°, (d) d = 63°, (e) e = 50°, f = 130°, (f) g = 75°, (g) h = 69°, (h) i = 67°, (i) j = 115°