Yahoo Answers: Answers and Comments for How to solve this geometry problem, with proof? [Mathematics]
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From Liam
enUS
Fri, 14 Apr 2017 06:47:11 +0000
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Yahoo Answers: Answers and Comments for How to solve this geometry problem, with proof? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20170414064711AACRcVu
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From Learner: i) By angle sum property from triangle MKN, &l...
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https://answers.yahoo.com/question/index?qid=20170414064711AACRcVu
Fri, 14 Apr 2017 14:00:39 +0000
i) By angle sum property from triangle MKN, <MKN = 55°
As given <MKP = 10°, <PKN = 45°
==> KN = PN  (1)
ii) <KNS = 90  20 = 70°
So from triangle KNS, by angle sum property, <KSN = 55°
==> Triangle KNS is isosceles. [<SKN = <KSN]
==> KN = SN  (2)
iii) Thus from (1) & (2): PN = SN
So triangle PSN is isosceles.
==> <NPS = <NSP = (180  20)/2 = 80°
So applying exterior angle property, from triangle PSM,
<PSM = 80°  <PMS = 80°  35° = 45°
Thus <PSM = 45°
NOTE: Irrespective of belated reply, wish you may acknowledge or provide a feed back subject to finding this solution satisfactory. Thanks.

From la console: Recall the rule: the sum of 3 angles of whatev...
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https://answers.yahoo.com/question/index?qid=20170414064711AACRcVu
Fri, 14 Apr 2017 09:31:59 +0000
Recall the rule: the sum of 3 angles of whatever the triangle is always 180 °.
To be clearer, we are going to use the colors instead name of angle.
In the triangle KNM, you know that this triangle is a right triangle at N.
red + cyan = 90
cyan = 90  red → given: red = 20
cyan = 70
In the triangle KNM, you apply the rule.
yellow + red + cyan + blue + green = 180 → we've just seen that: red + cyan = 90
yellow + 90 + blue + green = 180 → given: yellow = 35
35 + 90 + blue + green = 180 → given: green = 10
35 + 90 + blue + 10 = 180
135 + blue = 180
blue = 45
In the triangle KPM, you apply the rule.
purple + green + yellow = 180 → given: yellow = 35
purple + green + 35 = 180 → given: green = 10
purple + 10 + 35 = 180
purple + 45 = 180
purple = 135
In the triangle KAN, you apply the rule.
cyan + blue + orange = 180 → we've seen that: cyan = 70
70 + blue + orange = 180 → we've seen that: blue = 45
70 + 45 + orange = 180
115 + orange = 180
orange = 65
At the point A, you can deduce that:
grey = orange → we've just seen that: orange = 65
grey = 65
At the point A, you can see that:
grey + dark_green = 180 ← because it is a flat angle
dark_green = 180  grey → we've just seen that: orange = 65
dark_green = 115
In the triangle KAS, you apply the rule.
dark_green + green + brown = 180 → we've just seen that: dark_green = 115
115 + green + brown = 180 → given: green = 10
115 + 10 + brown = 180
125 + brown = 180
brown = 55
At the point S, you can deduce that:
brown + pink = 180 ← because it is a flat angle
brown + pink = 180 → we've just seen that: brown = 55
55 + pink = 180
pink = 125
At the point P, you can deduce that:
purple + white = 180 ← because it is a flat angle
purple + white = 180 → we've seen that: purple = 135
135 + white = 180
white = 45
In the triangle PSK, you apply the rule.
α + β + brown + green = 180 → we've seen that: brown = 55
α + β + 55 + green = 180 → given: green = 10
α + β + 55 + 10 = 180
α + β + 65 = 180
α + β = 115
α = 115  β ← memorize this result as (1)
In the triangle PSM, you apply the rule.
yellow + θ + (purple  α) = 180 → given: yellow = 35
35 + θ + (purple  α) = 180 → we've seen that: purple = 135
35 + θ + (135  α) = 180
35 + θ + 135  α = 180
θ + 170  α = 180
θ  α = 10
θ = 10 + α ← memorize this result as (2)
In the triangle PSM, you apply the rule.
yellow + γ + θ = 180 → given: yellow = 35
35 + γ + θ = 180
γ + θ = 145
γ = 145  θ → recall (2): θ = 10 + α
γ = 145  (10 + α)
γ = 145  10  α
γ = 135  α → recall (1): α = 115  β
γ = 135  (115  β)
γ = 135  115 + β
γ = 20 + β ← memorize this result as (3)
…now you have all the conditions to find the angle PSM, i.e. θ → θ = 45

From Captain Matticus, LandPiratesInc: I'm getting 147.5
https://answers.yahoo.com/question/index?qid=20170414064711AACRcVu
https://answers.yahoo.com/question/index?qid=20170414064711AACRcVu
Fri, 14 Apr 2017 07:21:56 +0000
I'm getting 147.5