(Photo with the question is attached)

Answer is the length of the arc PQ in millimetres.

Arc PQ measures 24mm.

Step-by-step explanation: If Arc AB measures 16, remembering that length of an arc is given as

Length of Arc = O/360 x 2πr

Where O is the size of the angle subtended by the arc. We should also note that angle C is the opposite of angle 60, therefore angle C equals 60°. Hence we can now express the length of Arc AB properly as,

16 = {60°/360°} x 2πr

16 = (1/6) x 2πr

By cross multiplication we now have

(16 x 6)/2 = πr

48 = πr

48/π = r

The radius of the larger circle has now been identified as 48/π.

If the radius of the small circle is given as ¾ of the larger circle's radius, then radius of small circle would be

Radius = 3/4 x 48/π

Radius = 36/π

Therefore to calculate the length of arc PQ (which by the way is in the smaller circle). Note that the angle subtended by arc PQ equals 180 - 60 which equals 120° {Sum of angles on a straight line equals 180}

PQ = O/360 x 2πr

PQ = (120/360) x 2π x (36/π)

PQ = (1/3) x 2π x (36/π)

PQ = (2π x 36)/(3 x π)

(π cancels out π, numerator and denominator)

PQ = 24

Therefore arc PQ equals 24 mm.

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

answer: i'm great at algebra

~coco

step-by-step explanation: