SOLUTION: We have a concave kite ABCD, there is an interior angle at vertex B that is a reflex angle. Given that m∠A = m∠C = m∠D = 30° and the length of side AB is 8 in, find

Question 1193075: We have a concave kite ABCD, there is an interior angle at vertex B that is a reflex angle.
Given that
m∠A = m∠C = m∠D = 30°
and the length of side
AB
is 8 in, find the length (in INCHES) of
AC

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

When the problem asks for the "length of AC", it implies that AC is a segment in the problem; but in kite ABCD, AC is not a side of the kite.

So I will assume the problem is only asking for the DISTANCE BETWEEN A and C.

Since three of the angles of the concave kite have measures of 30 degrees each, and since the sum of the interior angles of the kite is still 360 degrees, the measure of reflex angle B is 360-3(30)=270 degrees.

That means angle ABC is 360-270=90 degrees.

Then AC can be seen as the hypotenuse of an isosceles right triangle with side length 8, so the length of AC is 8*sqrt(2).

ANSWER: 8*sqrt(2)

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