Which statements are true? check all that apply. m = 120° m = 60° m∠cob = 2(m∠cab) m∠cob = 120° m∠cob = (m∠cab)

1. m =120° , m =60°¬ (incorrect) ⇒if you are considering a triangle sum of three angles should be 180°. Here sum of two angles is 180. Second thing you can't name the angles of a triangle by small letters.Thirdly two angles can't have same measure.

2.m∠COB = 2(m∠CAB)  ¬ Correct

Consider a triangle COB , AB being the base and O at a certain distance from A.So in this case this possibility is sure to happen.Shown through a diagram

3.m∠COB = 120° ¬ Correct ⇒Consider a triangle COB,∠COB can be obtuse.So we call it obtuse angled triangle.

4.m∠COB = m∠CAB ¬ Correct

To prove this i have given a diagram below.

A relationship between m∠COB and m∠CAB is that they subtend the same

arc on the circumference of the circle wit center at O.

The true statements are;

Reasons:

The possible diagram in the question created with MS Visio is attached.

From circle theorem we have, angle at the center = Twice angle formed at the circumference

m∠COB = The angle subtended by arc at the center

m∠CAB = The angle subtended by arc at the circumference of the circle

Therefore;

Which gives;

m∠COB = 2 × 60° = 120°

m∠COB = = 120°

Learn more about other circle theorems here:

link

75

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.