Question

Using the diagram, calculate the values of the unknown variables: a, b, and c.

Answer 1

Answer:

a = 82

b = 130

c = 118

Step-by-step explanation:

A quadrilateral is inscribed in a circle. So, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

a° + 98° = 180°

a° = 180° - 98°

a° = 82°

a = 82

By inscribed angle theorem:

a° = 1/2(b° + 34°)

82° * 2 = b° + 34°

164° - 34° = b°

b° = 130°

b = 130

Again by inscribed angle theorem:

76° = 1/2(c° + 34°)

76° *2 = c° + 34°

152° - 34° = c°

c° = 118°

c = 118