Question

Find the measure of arc FV

Answer 1

60 degrees

Explanation:

The measure of an inscirbed angle is half the measure of the intercepted arc.

(The measure of the arc is twice the measure of the angle!)

The inscribed angle at V intercepts an arc of 2 x 119 = 238 degrees, so the measure of arc FGH is 238. Subtract arc GH from that, 238 - 168 = 70, so that is the measure of arc FG.

The angle at H intercepts an arc with measure 2 x 65 = 130. The measure of arc VFG is 130. But arc FG is part of that, so subtract its measure from 130. 130 - 70 = 60.

The measure of arc FV is 60 degrees.

Answer 2

FV = 60

Explanation:

VG => 65 × 2 = 130

FH major arc=> 119 × 2 = 238

FH major arc - GH = FG

FG => 238 - 168 = 70

VG - FG major arc = FV

FV => 130 - 70 = 60