## Exam-Style Questions on Angles## Problems on Angles adapted from questions set in previous Mathematics exams. |

## 1. | GCSE Higher |

The exterior angle of a regular polygon is 72°

What is the name of the regular polygon?

## 2. | GCSE Higher |

The points B, C, D, E and F are on a circle. DAE and CAB are straight lines and AB= BE.

Calculate the value of \(x\).

## 3. | GCSE Higher |

The points B, C, D and E lie on the circle with centre at A.

FBE is a straight line.

DC = BC

BE = EC

Angle DCB is 35°

Find angle DBF.

You must give a reason for each stage of your working.

## 4. | GCSE Higher |

The diagram, not drawn to scale, show a polygon with one line of symmetry, AE.

Angle HAB is 90° and interior angle DEF is 220°.

Work out the size of angle ABC which is half the size of interior angle BCD and twice the size of angle CDE.

## 5. | GCSE Higher |

A number of regular pentagons and squares are arranged around the outside of a large blue regular polygon. Just the lower part of the arrangement is shown below.

How many sides does the large blue regular polygon have?

## 6. | GCSE Higher |

The diagram below shows two parallel lines, AB and CD, crossed by a transversal line EF. Find the values of \(w\), \(x\) and \(y\).

.All angles are in degrees.

## 7. | GCSE Higher |

In the following diagram AD is parallel to CE and AD = CD. Angle AFD is a right angle.

The diagram is not drawn to scale.

Calculate the size of angle DCE.

## 8. | GCSE Higher |

B, C, D and E are points on the circumference of a circle, centre O.

BD is a diameter of the circle and the diagram is not drawn to scale.

(a) Find the size of angle DBE and give a reason for your answer.

(b) Find the size of angle DBC and give a reason for your answer.

## 9. | GCSE Higher |

A point P is marked on side BC of parallelogram ABCD such that AB = BP.

Find the value of angle \(x\).

## 10. | IGCSE Extended |

In the diagram above, not drawn to scale, A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 28°.

Calculate

(a) angle AOT

(b) angle ACB

(c) angle ABT

## 11. | GCSE Higher |

PQRS is a rhombus and C is the midpoint of QS.

The angle QRS is 120^{o} and A is the point on QS such that PA = AQ.

Calculate the size of angle CPA.

## 12. | IGCSE Extended |

The diagrams are not drawn to scale

ABCDEF is a hexagon with AB parallel to ED and BC parallel to FE. GFE and GABH are straight lines. Angle CBH = 70 Calculate the values of: (a) \(p\); (b) \(q\); (c) \(t\); (d) \(x\). |
K, P, J and N are points on a circle and KN = NP. KJ is a diameter and LKM is the tangent to the circle at K. Angle LKN = 59 Find the values of: (e) \(y\); (f) \(z\). |

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