Geometry and measurementGrades 4–8
Triangles worksheet: missing angles and classification
Draws triangles with their angles marked. Students find a missing angle using the 180° rule, or name each triangle as equilateral, isosceles or scalene and as acute, right or obtuse. Answer key included.
- Fresh problems every time
- Answer key on its own page
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On this page
Two skills on one shape
Triangles can be described in two ways. By their angles, a triangle is acute (all three less than 90°), right (one exactly 90°) or obtuse (one more than 90°). By their sides, it is equilateral (three equal), isosceles (two equal) or scalene (none equal). Separately, the three angles of every triangle add to 180°, which lets you find a missing one by subtraction.
The generator makes both kinds of sheet. They span grades 4 to 8: classifying is typically a fourth-grade skill, and using the angle sum comes later. The classification version works well after students know how to measure or compare angles, and the missing-angle version connects naturally to vertical angles.
Settings
This page uses the shared angle generator, and the Problems menu decides the task:
- Missing angle in a triangle. The preset. Each triangle shows all three angles, but one reads x. Students add the two known angles and subtract from 180°. Which of the three vertices is hidden changes from problem to problem, so students cannot assume x is always at the top.
- Classify triangles. All three angles are given, and the student fills in two words: the side type and the angle type. The sides are not marked with tick marks. Students must use the rule printed in the instruction line, that equal angles mean equal sides. A triangle with angles 60°, 60° and 60° is therefore equilateral, and two matching angles mean isosceles.
- Number of problems. Four to 16, with eight as the default. Use more for a mixed review.
The "Mixed missing angles" option includes triangle problems among other angle facts, but it does not include classification.
Worked example: angles 52° and 76°
Finding x.
- Add the two angles you know: 52 + 76 = 128.
- Subtract from 180: 180 − 128 = 52.
- So x = 52°.
Classifying the same triangle.
- The angles are 52°, 52° and 76°. Two are equal, so the triangle is isosceles.
- The biggest angle is 76°, less than 90°, so every angle is acute.
- The answer is "isosceles, acute."
That the missing angle equals one of the others is a nice moment to point out: the triangle has a hidden symmetry that the angle sum revealed.
What to check on the key
- Adding to 360° or 90°. The student's x is far too large or too small. A triangle's angles always total 180°.
- Forgetting to subtract. Writing 128° for x, the sum of the known angles.
- Classifying by looks. Drawings are fitted to the page, so students should trust the numbers, not their eyes. A pair of 40° angles means equal sides even if the picture seems a little lopsided.
- Mixing up the two word pairs. Writing "scalene, equilateral." One word describes sides, the other angles. The key always lists the side word first.
- Calling an acute triangle "right." A right triangle needs an angle of exactly 90°.
Note on right triangles
Because the angles in classify mode are generated at random, a right angle appears only now and then. To practice right triangles specifically, use the missing-angle mode and ask students to say what kind of triangle they have after finding x. Once angles feel secure, area of triangles is the natural next step, since it asks for a different measurement of the same shape.