Angles in Shapes

AC is a tangent to the circle, centre O, with point of contact B.
DE is a diameter of the circle and F is a point on the circumference.
Angle ABD is 77° and angle DEF is 64°.

Calculate the size of angle BDF.

The diagram below shows a circle, centre O.

AB and CB are tangents to the circle.
AC and ED are parallel.
Angle AOD is $\displaystyle 143^{\circ}$.
Calculate the size of angle ABC.

In the diagram:
ABE is a tangent to the circle centre O.
Angle DBE is $\displaystyle 58^{\circ}.$

Calculate the size of angle CAB.

The diagram below shows a circle with centre O.
AB is a tangent to the circle at the point C.
CD is a diameter of the circle.
Angle EOD is $\displaystyle 68^{\circ}$.

Calculate the size of angle ACE.

A logo consists of an H shape and a regular decagon.
The diagram represents the logo.

Calculate the size of the shaded angle.

The diagram below shows a circle centre O.

• AC is a tangent to the circle at the point B.
• CE is a tangent to the circle at the point D.
• DG and BF are diameters of the circle.
• Angle DFE is 125°.
Calculate the size of shaded angle BCD.

In the diagram, ABCDE is a regular pentagon.
• Angle EFA is 65°.
• FAB is a straight line.

Calculate the size of angle FEA.