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Welp this question is eating my brain

Welp this question is eating my brain-example-1

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Hello!

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(a) y = 36° and x = 36°

DAB = 90°

so y = 90° - 54° = 36°

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AB // DC

so x and y are alternate-internal

so x = y = 36°

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(b) y = 73° and x = 68°

SPQ = 90°

so yPQ = 90° - 51° = 39°

the sum of the angles of the triangle PQR = 180°

so y = 180° - (39° + 68°) = 73°

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PSy = 90°

the sum of the angles of the triangle PSy = 180°

so PyS = 180° - (51° + 90°) = 39°

SyxR is a flat angle = 180°

so x = 180° - (39° + 73°) = 68°

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(c) y = 36° and x = 54°

The center of the triangle is K.

So the triangles NKO, MKP, MNK, POK are isosceles

NKO = MKP and MNK = POK

MKP and NKO are opposed

so MKP = NKO = 72°

K is a full angle = 360°

so MKN and PKO = 360° - (72° + 72°) = 216°

so MKN = PKO = 216°/2 = 108°

PMN = y so because MKN is isoscel.

so we know x + y = 90° because PMN = 90°

and so we know PON = OPM = y

and so we know KNO = KON = x

the sum of the angles of the triangle KNO = 180°

so KNO and KON = 180° - 72° = 108°

so x = 108°/2 = 54°

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the sum of the angles of the triangle MKN = 180°

so KMN and KNM = 180° - 108° = 72°

so y = 72°/2 = 36°

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User Yokich
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