2. what is the radius of a circle if the length of a 45° arc is

11.46

Step-by-step explanation:

Formula for calculating the length of an arc is theta/360 ×2Πr. Where;

length of the arc (L) = 9

Theta= 45°

L = theta/360 × 2Πr

9 = 45/360× 2Πr

9 = 1/8 × 2Πr

9 = Πr/4

Πr = 36

r = 36/Π

r = 11.46

Substituting we have,

9 = r × 45°

r = 9/45

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

answer: your correct answer is b. d.

step-by-step explanation: