Answer:
Step-by-step explanation:
ΔAOC is an isosceles triangle as OC = OA ----> RADIUS
42 + 42 + ∠AOC = 180 {Angle sum property}
84 + ∠AOC = 180
∠AOC = 180 - 84
∠AOC = 96°
y = 96/2 {Central angle theorem}
y = 48° ------------(I)
∠B + ∠D = 180 {sum of opposite angles of Cyclic Quadrilateral}
x + y = 180
x + 48 = 180 {from (I) }
x = 180 - 48
x = 132°
Assuming your 10N are all intended to be 10^N, equations B, D, F are correct.
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Your calculator can help you with this.
I want you to imagine as you read this or you can draw through the help of my explanation and see yourself:
1↪Draw triangle ABC where BC>AC
2↪D is any point on AC such that CD=CB
3↪Roughly drawing , you can assume CD=CB and and join BD
4↪SO triangle ABC which is a big triangle is divided into Triangles ABD and BDC
5↪See in triangle BDC ,CD=CB so, base angles of isosceles triangle are equal:
<CDB=<CBD = x (assume) which means x is acute angle since CDB and CBD are are in same triangle with same measure and there can't be any two obtuse angle in any traingle. So x must be acute.
6↪Now see in traingle ABD,
<ADB=180-<CDB=180-x=obtuse angle
...check yourself ...just subtract any acute angle from 180 you will get only obtuse angle (ie angle greater than 90)
That means in triangle ABD , one angle ADB is obtuse which means remaining <ABD and < BAD are acute. [PROVED]
❇Main Concept Used Here:
↪In any triangle there can be maximum of one obtuse angle...so remaining two must be acute angle otherwise interior angles sum can't be equal to 180.
This is an math/way answer, and I don't have an explanation to the problem, but I hope this is good enough.
Since 5*6 = 30 and 3^2*3.14=9*3.14=28.26 and 30 + 28.26 = 58.26 the answer is 58.26.
