15+ points for best

1. segment ad is a diameter of circle t.

if tb is 6 cm long, m∠ate = 94°, m∠btc = 56°, and m∠ctd = 32°, what is the length of arc cd?

[see attachment if necessary]

a. 32 cm

b. 3.35 cm

c. 1.07 cm

d. 1.67 cm

2. if m∠dac = 31° and m∠cab = 27°, what is the measure of arc bd?

[see 2nd attachment if necessary]

arc bd = °

1) mesure of an arc= R.Ф, where R is the radius & Ф the angle IN RADIAN

32°===>8π/45 OR 0.5585, So mes of Arc CD = 6x0.5585 = 3.35 cm

2) DAC = 31° & CAD =27° , these 2 angles being adjacent I can write that

Angle(DAC +CAB=DCB) ==>Angle DCB =(31°+27°=58°)

To remember that any vertex of an angle on the circles, its sides intercept an arc which mesure is twice the angle,

Hence since mes Angle DCB=58°, that means the ARC intercepted, namely DB has a length of 2x 58 = 116°