In a parallelogram FIST, find ZSFT, ZOSTand ZSTO.110°359

1.	In a parallelogram FIST, find ZSFT, ZOSTand ZSTO.110°359
Answer» In a Parellelogram oppsite sides are parellel then ∠SIF = 60 degree ∠SIF + ∠IFT = 180 degree ( Co interior angles) ∠IFT = 120 degree ∠ITF = ∠TIS = 25 degree ( Alternate angles ) ∠ITF = ∠OTF ( same measure. Anyone can see) if ∠TOF = 110 degree And ∠OTF = 25 degree Sum of the angles of Triangle FOT = 180 degree ( Angle sum property of a triangle) ∠FOT + ∠OTF + ∠OFT = 180 degree 110 degree + 25degree + ∠OFT = 180degree ∠OFT = 180 degree - 135 degree = 45 degree = ∠ SFT We already know ∠IFT = 120 degree and ∠SFT = 45 Degree then ∠IFS = 120 degree - 45 degree = 75 degree ∠IFS = ∠OST ( alternate angles) ∠OST = 75 degree ∠FOT + ∠TOS = 180 degree ( Linear Pair) 110 degree + ∠Tos = 180 degree ∠Tos = 180 - 110 degree ∠Tos = 70 degree ∠TOS + ∠OST + ∠STO = 180 degree ( Angle sum property of a triangle) 70 degree + 75 degree + ∠STO = 180 degree ∠STO + 145 Degree = 180 degree ∠STO = 180 degree - 145 degree = 35 Degree

Answer»

In a Parellelogram oppsite sides are parellel then

∠SIF = 60 degree

∠SIF + ∠IFT = 180 degree ( Co interior angles)

∠IFT = 120 degree

∠ITF = ∠TIS = 25 degree ( Alternate angles )

∠ITF = ∠OTF ( same measure. Anyone can see)

if ∠TOF = 110 degree And ∠OTF = 25 degree

Sum of the angles of Triangle FOT = 180 degree ( Angle sum property of a triangle)

∠FOT + ∠OTF + ∠OFT = 180 degree

110 degree + 25degree + ∠OFT = 180degree

∠OFT = 180 degree - 135 degree = 45 degree = ∠ SFT

We already know ∠IFT = 120 degree and ∠SFT = 45 Degree

then ∠IFS = 120 degree - 45 degree = 75 degree

∠IFS = ∠OST ( alternate angles)

∠OST = 75 degree

∠FOT + ∠TOS = 180 degree ( Linear Pair)

110 degree + ∠Tos = 180 degree

∠Tos = 180 - 110 degree

∠Tos = 70 degree

∠TOS + ∠OST + ∠STO = 180 degree ( Angle sum property of a triangle)

70 degree + 75 degree + ∠STO = 180 degree

∠STO + 145 Degree = 180 degree

∠STO = 180 degree - 145 degree = 35 Degree

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