∠A and \angle B∠B are complementary angles. If m\angle A=(2x-10)^{\circ}∠A=(2x−10) ∘ and m\angle B=(x-2)^{\circ}∠B=(x−2) ∘ , then find the measure of \angle A∠A.

118°

Step-by-step explanation:

Two angles are called complementary when their measures add to 90 degrees.

From the question,

Angle A=(2x-10)°

Angle B=(x-2)°

Both Angles are complementary.

Therefore

Step 1

(2x - 10)° + (x - 2)° = 180°

2x + x - 10 - 2 = 180°

3x - 12 = 180°

3x = 180° + 12

3x = 192°

x = 192/3

x = 64°

Step 2

We are to solve for Angle A

(2x-10)°

Angle A = 2(64 ) - 10

Angle A = 128 - 10

Angle A = 118°

The measure of Angle A = 118°

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.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm