Geometry
GradesGrade 7GeometryAngle Sums: Triangles and Quadrilaterals

Angle Sums: Triangles and Quadrilaterals

📐 Geometry
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Angle Sums: Triangles and Quadrilaterals

Every triangle's interior angles sum to 180°, and every quadrilateral's to 360°!

No matter the shape or size, the interior angles of ANY triangle always sum to exactly 180°. For quadrilaterals (4-sided polygons), they always sum to 360°. These facts let you find any missing angle if you know the others.

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Triangle angles: sum = 180°. Quadrilateral angles: sum = 360°.

🔺Finding a missing triangle angle
A triangle has angles of 50° and 70°.
Third angle = 180° − 50° − 70° = 60°.

Check: 50° + 70° + 60° = 180° ✓
🟦Finding a missing quadrilateral angle
A quadrilateral has angles of 90°, 85°, and 110°.
Fourth angle = 360° − 90° − 85° − 110° = 75°.

Check: 90 + 85 + 110 + 75 = 360° ✓

Types of triangles by angle:

Acute: all angles < 90°Right: one angle = 90°Obtuse: one angle > 90°

Regardless of type, all three interior angles always total 180°!

Finding a missing interior angle:

1Identify the shape: triangle (total 180°) or quadrilateral (total 360°)
2Add all the KNOWN angles together
3Subtract that sum from the total (180° or 360°)
4The result is the missing angle
✏️ Try It!

A triangle has two angles measuring 45° and 80°. What is the third angle?

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Remember This!

A triangle can never have two right angles — that would already equal 180° with no room for the third! And a triangle with an obtuse angle must have two acute angles to compensate.

Take Quiz 📝 — 25 Questions