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

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