Geometry and measuresGCSE / IGCSE

Angles in a trapezium with algebra

Build equations from parallel sides or equal base angles.

  • Use a total of for angles along the same non-parallel side.
  • Equate base angles only when the trapezium is isosceles.

Example 1

Find in the trapezium.

These angles lie on the same side of a transversal between parallel sides, so they add to 180°.Apply this to both sides.Apply this to both sides.
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.
Apply this to both sides.Apply this to both sides.

Example 2

Find in the isosceles trapezium.

The base angles of an isosceles trapezium are equal.Apply this to both sides.
The base angles of an isosceles trapezium are equal.
Apply this to both sides.

Your turn

Question 1

Find in the trapezium.

Check answer
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.Apply this to both sides.Apply this to both sides.
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.
Apply this to both sides.Apply this to both sides.
Question 2

Find in the isosceles trapezium.

Check answer
The base angles of an isosceles trapezium are equal.Apply this to both sides.
The base angles of an isosceles trapezium are equal.
Apply this to both sides.
Question 3

Find in the trapezium.

Check answer
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.Apply this to both sides.Apply this to both sides.
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.
Apply this to both sides.Apply this to both sides.
Question 4

Find in the isosceles trapezium.

Check answer
The base angles of an isosceles trapezium are equal.Apply this to both sides.
The base angles of an isosceles trapezium are equal.
Apply this to both sides.
Question 5

Find in the trapezium.

Check answer
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.Apply this to both sides.Apply this to both sides.
These angles lie on the same side of a transversal between parallel sides, so they add to 180°.
Apply this to both sides.Apply this to both sides.
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