Help your students prepare for their Maths GCSE with this free missing angles in a quadrilateral worksheet of 44 questions and answers
The interior angle sum in a quadrilateral is based on the axiom or postulate that (in standard Euclidean geometry) the sum of interior angles of a triangle is 180°. As any quadrilateral can be split into two triangles, the sum of the angles in any quadrilateral is 360°. This fact can be used to find an unknown angle in a quadrilateral, by summing the other angles and subtracting the total from 360°. This is useful when a diagram is not drawn to scale, so protractors or angle measures cannot be used.
Special quadrilaterals such as squares, rectangles and parallelograms have particular angle properties that should be used when solving these problems. For example, it is assumed that students will recognise right angles when marked at the vertices on a diagram, so these will not be given in figures. Similarly, they need to be able to recognise the markings for parallel lines. Opposite angles in a parallelogram are equal, as are base angles in an isosceles triangle, so these facts about known angles might be needed to solve some problems.
Angle problems don’t usually contain difficult fractions and decimals, but answers often need to be rounded to a given degree of accuracy.
Angles of a quadrilateral can be extended further to applications involving algebraic expressions and solving equations.
Looking forward, students can then progress to finding the size of angles in polygons, finding exterior angles, and using angle facts for parallel lines. There are also additional geometry practice worksheets available for a variety of other topics.
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