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