quadrilateral abcd is inscribed in this circle. what is the measure of ∠a ? enter your answer in the box.

The answer is 137°.

Step-by-step explanation: Given that the quadrilateral ABCD is inscribed in a circle, where measure of angle C is 43°. We are to find the measure of ∠A.

Since the quadrilateral ABCD is inscribed in a circle, so it will be a cyclic quadrilateral. Also, the sum of opposite angles of a cyclic quadrilateral is 180°.

Therefore, we have

Thus, the required answer is 137°.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the answer is 8.64

step-by-step explanation: