Find the missing angle for the irregular polygon. show your work.

x = 114 , ∠A = 132 , ∠B = 114 and ∠D = 124

Step-by-step explanation:

The polygon has 7 sides

A 7 sided polygon has angles that add up to 900 degrees.

So if we add all the measures of the angles and set it to 900 we can solve for x

900 = x + 18 + 132 + 130 + 130 + x + 10 + 138 + x

step 1 : combine like terms

18+132+130+130+10+138 = 558

x + x + x = 3x

We now have 3x + 558 = 900

step 2 : subtract 558 from both sides

900 - 558 = 342

we then acquire 342 = 3x

step 3 : divide both sides by 3

342 / 3 = 114 and 3x / 3 = x

we're left with x = 114

Now we plug in the value of x into the x's to find the measures of the unknown angles

∠B = x and x = 114 so ∠B simply has a measure of 114°

∠A = x + 18

x = 114

∠A = 114 + 18 = 132°

∠D = x + 10

x = 114

∠D = 114 + 10 = 124°

So we can conclude x = 114 , ∠A = 132 , ∠B = 114 and ∠D = 124

yes

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.