Question

If M/DFC= 40 and M CD= 55 the BG=
25
80
135

Answer 1

25

Explanation:

GC and BD are 2 intersecting chords thus the measure of the angle formed is

∠DFC = 0.5( m arc CD + m arc BG ), that is

0.5(55 + BG) = 40 ( multiply both sides by 2 )

55 + BG = 80 ( subtract 55 from both sides )

BG = 25

Answer 2

BG = 25°

Explanation:

Given

∠DFC=40°

arc CD=55°

The inner angle of an arc is calculated by the semi-sum of the arcs comprising it and its opposite.

Mathematically, it is represented as follows;

∠DFC=½[CD+BG]

Open bracket

∠DFC=½ CD+½ BG]l

Make arc BG the subject of formula

½ BG = ∠DFC - ½CD

Multiply both sides by 2

BG = 2∠DFC - arc CD

By substituton,

BG = 2 * 40 - 55

BG =80°-55°

BG =25°

Hence the measurement of Arc BG is 25°