Question

11. AB and CD are chords of this circle, centre O. AD is a straight line.
Calculate the values of angles a - f.

Can anyone help?? it’s really urgent!

Answer 1

The values of the angles a - f are

a = 47°

b = 86°

c = 47°

d = 47°

e = 86°

f = 8°

Calculating angles in a circle

From the question, we are to determine the values of angles a - f.

• For a

In the diagram,

/AO/ = /BO/ (They are radii of the circle)

Then,

ΔAOB is an isosceles triangle

∴ a = 47° (Base angles of an isosceles triangle)

• For b

b + a + 47° = 180° (Sum of angles in a triangle)

b + 47° + 47° = 180°

b + 94 = 180°

b = 180° - 94°

b = 86°

• For c

Since AB = CD

Then, ΔAOB and ΔCOD are similar triangles

By comparison,

c = 47°

• For d

c = d (Base angles of an isosceles triangle)

d = 47°

• For e

e = 86° (By comparison)

• For f

b + f + e = 180° (Sum of angles on a straight line)

86° + f + 86° = 180°

f + 172° = 180°

f = 180° - 172°

f = 8°

Hence, the values of the angles a - f are

a = 47°

b = 86°

c = 47°

d = 47°

e = 86°

f = 8°

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