Math worksheet for calculating missing angles in triangles, featuring eight problems with various triangle types and angle measurements.

Let’s solve each triangle one by one. Remember: the angles in any triangle always add up to 180°. We’ll use that rule for every problem.

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Problem 1)
We have a right triangle (one angle is 90°) and another angle is 35°.
So, missing angle = 180° - 90° - 35° = 55°

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Problem 2)
Two angles given: 32° and 28°.
Missing angle = 180° - 32° - 28° = 120°

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Problem 3)
It says “Isosceles” — that means two angles are equal. The top angle is 124°.
So the other two angles together = 180° - 124° = 56°
Since they’re equal, each one = 56° ÷ 2 = 28°

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Problem 4)
Angles given: 136° and 25°.
Missing angle = 180° - 136° - 25° = 19°

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Problem 5)
Right triangle again (90°), and one angle is 31°.
Missing angle = 180° - 90° - 31° = 59°

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Problem 6)
Isosceles triangle. One angle is 67°. Since it’s isosceles, either:
- The 67° is one of the two equal angles → then the other equal angle is also 67°, and the third is 180° - 67° - 67° = 46°
- OR the 67° is the unique angle → then the other two are equal: (180° - 67°) ÷ 2 = 56.5°

But looking at the diagram (even though not to scale), the 67° is at the top, and the base angles look like they should be equal — so likely the 67° is the *unique* angle? Wait — actually, in most textbook diagrams for isosceles triangles, if only one angle is labeled and it’s not at the base, it’s often the vertex angle. But let’s check both possibilities.

Wait — actually, in Problem 6, the 67° is shown at the top, and the two bottom angles are marked with arcs — meaning they are the equal ones! So the 67° is the *vertex* angle, and the two base angles are equal.

So: total of base angles = 180° - 67° = 113°
Each base angle = 113° ÷ 2 = 56.5°

But wait — 56.5° is not a whole number. Let me double-check the diagram description. Actually, in many such worksheets, they avoid decimals unless necessary. Maybe I misread.

Looking back: In Problem 6, the 67° is at the top, and the two bottom angles are marked with single arcs — which usually means they are equal. So yes, 67° is the vertex angle.

So: 180 - 67 = 113; 113 / 2 = 56.5 → but maybe we leave it as 56.5° or 56½°? However, let’s see if there’s another interpretation.

Alternatively, perhaps the 67° is one of the base angles? Then the other base angle is also 67°, and the top is 180 - 67 - 67 = 46°. That gives whole numbers.

Which is more likely? In standard problems, if an isosceles triangle has one angle labeled and it’s acute, and no indication otherwise, sometimes it’s assumed to be a base angle. But here, since the arc marks are on the two bottom angles, that suggests those are the equal ones — so the 67° must be the top angle.

Actually, re-examining: in the original image description, for Problem 6, it says “Isosceles” and shows 67° at the top, and the two bottom angles have matching arc marks — so yes, the two bottom angles are equal, and 67° is the vertex.

So answer is 56.5° for each base angle. But let’s confirm calculation:

67 + 56.5 + 56.5 = 67 + 113 = 180 → correct.

But maybe the worksheet expects fractional form? Or perhaps I made a mistake.

Wait — let me check online or think differently. Actually, in some curricula, they might expect you to write 56.5° or 56½°. But let’s proceed.

However, upon second thought — in Problem 3, they had 124° and got 28° each — which is fine. Here, 56.5° is acceptable.

But let’s hold on — maybe I misidentified. Another way: perhaps the 67° is one of the equal angles? Then the other equal angle is 67°, and the third is 46°. And 46° is a nice number.

Looking at the diagram mentally: if the 67° is at the top, and the triangle looks wide at the bottom, then the base angles would be smaller — but 56.5° is still reasonable.

Actually, let’s calculate both:

Option A: 67° is vertex → base angles = (180-67)/2 = 56.5° each
Option B: 67° is base → other base = 67°, vertex = 46°

In the absence of clear diagram, but since the problem says "Isosceles" and labels only one angle, and in many textbooks, when they label the vertex angle, they specify, but here it's ambiguous.

Wait — looking back at the user's image description: for Problem 6, it says "6) Isosceles" and shows a triangle with 67° at the top, and the two bottom angles have identical arc markings — which universally means those two angles are equal. Therefore, the 67° is NOT one of the equal angles — it’s the different one.

So yes, the two bottom angles are equal, and their sum is 180 - 67 = 113, so each is 56.5°.

But 56.5° is 56 and a half degrees. We can write it as 56.5° or 56½°.

I think for this level, they might accept 56.5°.

But let’s move on and come back.

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Problem 7)
Angles given: 21° and 18°.
Missing angle = 180° - 21° - 18° = 141°

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Problem 8)
Right triangle (90°), and one angle is 66°.
Missing angle = 180° - 90° - 66° = 24°

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Now back to Problem 6. Let me verify with logic. If the two base angles are equal and marked with arcs, and the top is 67°, then yes, each base angle is (180-67)/2 = 56.5°. Perhaps the worksheet allows decimal answers.

Maybe I should write it as 56.5°.

But let’s list all answers clearly.

Final Answers:

1) 55°
2) 120°
3) 28° (each of the two equal angles)
4) 19°
5) 59°
6) 56.5° (each of the two equal base angles)
7) 141°
8) 24°

For Problem 6, since it's isosceles and the two base angles are equal, and the vertex is 67°, then each base angle is 56.5°. I think that's correct.

Perhaps the problem intends for us to realize that 67° is a base angle? But the arc marks suggest otherwise.

To resolve: in standard notation, if two angles have the same arc mark, they are equal. In Problem 6, the two bottom angles have the same arc, so they are equal, and the top is 67°, so yes.

So I'll go with 56.5°.

But let's write it as a fraction: 113/2 = 56.5, so 56.5° is fine.

Now, compiling all:

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Final Answer:
1) 55°
2) 120°
3) 28°
4) 19°
5) 59°
6) 56.5°
7) 141°
8) 24°