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Quadrilateral Exterior Angles Worksheet

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Quadrilateral Exterior Angles Worksheet

A quadrilateral has four exterior angles, one at each vertex. If you travel around the shape and take one exterior angle at each vertex, their sum is 360°. Show your working for calculation questions. Angles are in degrees (°).

Part A: Find the missing turn

Use the 360° total to solve each puzzle.

1.Three exterior angles of a rectangle are 90°, 90° and 90°. What is the fourth exterior angle?

2.A four-sided park sign has exterior angles of 82°, 96° and 105°. Calculate its fourth exterior angle.

3.A quadrilateral has exterior angles 110°, 70°, 95° and 85°. These angles make one full turn.

TrueFalse

4.Three exterior angles are 125°, 65° and 80°. Which value completes the quadrilateral?

80°
90°
100°
110°

Part B: Use clues

Set up an equation or use the 360° total to crack each puzzle.

5.A quadrilateral has exterior angles 90°, 110°, x° and x°. Find x.

6.The exterior angles of a quadrilateral are 75°, 105°, p° and q°. The last two angles are equal. Find p and q.

7.A quadrilateral has exterior angles 100°, 80°, r° and s°. The clue says r is twice s. Find r and s.

8.The four exterior angles are (x + 20)°, (x + 40)°, (2x − 10)° and (x + 50)°. Find x and then calculate all four angles.

Part C: Explain and create

Show how you know, not just what you calculate.

9.Why do the exterior angles of any quadrilateral add to 360°? Explain using the idea of turning as you travel once around the shape.

10.Choose three different exterior angles for a quadrilateral, then calculate a fourth angle that makes the total 360°. Write all four angles and show your addition.