Exam-Style Questions on Angles
Problems on Angles adapted from questions set in previous Mathematics exams.
The exterior angle of a regular polygon is 72°
What is the name of the regular polygon?
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 \(x\).
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.
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.
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?
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.
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.
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.
A point P is marked on side BC of parallelogram ABCD such that AB = BP.
Find the value of angle \(x\).
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°.
(a) angle AOT
(b) angle ACB
(c) angle ABT
PQRS is a rhombus and C is the midpoint of QS.
The angle QRS is 120o and A is the point on QS such that PA = AQ.
Calculate the size of angle CPA.
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 = 70o and angle EFA = 90o.
Calculate the values of:
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 = 59o.
Find the values of:
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