Question

What is the value of x?



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Answer 1

Hello!

The sum of all angle measures in a heptagon in 900°. We will subtract all of these angles from 900 to find our answer.

900-146-122-142-140-110-142=98

x=98°

I hope this helps!

Answer 2

Use (n - 2) × 180 to find the sum of the measures of the interior angles of the polygon, where n = number of sides of the polygon.
The polygon has 7 sides, so plug 7 in for n.

(7 - 2) × 180 = 900
The sum of the interior angles of this 7-gon is 900°.

Now that we know this, make an equation where all the interior angles add up to 900, then solve for x.

∠A + ∠B + ∠C + ∠D + ∠E + ∠F + ∠G = 900° ⇒
146 + 122 + 142 + 140 + 110 + 142 + x = 900
802 + x = 900
Subtract 802 from both sides.

x = 98°