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Opposite Angles

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 18 of 61.

Go round a parallelogram one corner at a time. With ∠A = 70°, the neighbour ∠B is 110°. The next neighbour, ∠C, is 180 − 110, which is 70° again, and ∠D is 110°.

$Parallelogram with angles 70, 110, 70 and 110 degrees$

So opposite angles of a parallelogram are equal. They are two steps apart round the shape, and each step takes 180° minus the angle before. The four angles still add up to 360°: 70 + 110 + 70 + 110.

The board has no single rule for opposite angles. Go round the corner instead: two steps of Co-interior angles, one along each side.

Challenge

ABCD is a parallelogram with ∠ABC = 124°. Find ∠ADC, marked ?, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons From an Angle to the Sides Inside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with x Regular Shapes Together Recap: Polygon Chases