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Question-226194




Question Number 226194 by fantastic2 last updated on 22/Nov/25
Answered by gregori last updated on 22/Nov/25
  ∡  = 60°     ∡  = 60°     ∡  = 360°−(2×120°+60°) = 60°
$$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{360}°−\left(\mathrm{2}×\mathrm{120}°+\mathrm{60}°\right)\:=\:\mathrm{60}°\: \\ $$
Commented by fantastic2 last updated on 22/Nov/25
pls expalin more :)
$$\left.{pls}\:{expalin}\:{more}\::\right) \\ $$
Commented by mr W last updated on 22/Nov/25
it is only given RS=((PQ)/2).  it is not given RS//PQ.
$${it}\:{is}\:{only}\:{given}\:{RS}=\frac{{PQ}}{\mathrm{2}}. \\ $$$${it}\:{is}\:{not}\:{given}\:{RS}//{PQ}. \\ $$
Commented by fantastic2 last updated on 22/Nov/25
sir pls ans i cant do it
$${sir}\:{pls}\:{ans}\:{i}\:{cant}\:{do}\:{it} \\ $$
Commented by fantastic2 last updated on 22/Nov/25
Q226143 what do you think  abt this q sir
$${Q}\mathrm{226143}\:{what}\:{do}\:{you}\:{think} \\ $$$${abt}\:{this}\:{q}\:{sir} \\ $$
Answered by mr W last updated on 22/Nov/25
Commented by mr W last updated on 22/Nov/25
(180°−2α)+60°+(180°−2β)=180°  ⇒α+β=120°  γ=180°−(α+β)=60°
$$\left(\mathrm{180}°−\mathrm{2}\alpha\right)+\mathrm{60}°+\left(\mathrm{180}°−\mathrm{2}\beta\right)=\mathrm{180}° \\ $$$$\Rightarrow\alpha+\beta=\mathrm{120}° \\ $$$$\gamma=\mathrm{180}°−\left(\alpha+\beta\right)=\mathrm{60}° \\ $$
Commented by fantastic2 last updated on 22/Nov/25
thanks sir
$${thanks}\:{sir} \\ $$
Answered by Kademi last updated on 22/Nov/25
      RS = (1/2)PQ  ⇒  (1/2)RS = (1/4)PQ  ⇔ Ro = (1/2)PO   let OR = 1   OR = PO   sin θ = ((Ro)/(PO))  ⇔ sin θ = (1/2)  →  θ = 30°   → RTQ = 2RTO   → ∡PTQ = 60°
$$\: \\ $$$$ \\ $$$$\:\mathrm{RS}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{PQ}\:\:\Rightarrow\:\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{RS}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{PQ}\:\:\Leftrightarrow\:\mathrm{Ro}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{PO} \\ $$$$\:{let}\:\mathrm{OR}\:=\:\mathrm{1} \\ $$$$\:\mathrm{OR}\:=\:\mathrm{PO} \\ $$$$\:\mathrm{sin}\:\theta\:=\:\frac{\mathrm{Ro}}{\mathrm{PO}}\:\:\Leftrightarrow\:\mathrm{sin}\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\rightarrow\:\:\theta\:=\:\mathrm{30}° \\ $$$$\:\rightarrow\:\mathrm{RTQ}\:=\:\mathrm{2RTO} \\ $$$$\:\rightarrow\:\measuredangle\mathrm{PTQ}\:=\:\mathrm{60}° \\ $$
Commented by fantastic2 last updated on 22/Nov/25
how you make the picture
$${how}\:{you}\:{make}\:{the}\:{picture} \\ $$
Commented by Kademi last updated on 22/Nov/25
 With patience and persistance.     Click on the left side menu, select Inserct Drawing,   then you really have to figure out how it all works.   It′s really quite a torture.   I woudn′t recomend doing this, unless you are   a person with iron made nervse like I am.        P.S. If anyway you try. To get out from drawing   creation, open again left menu and select    Enable Vertical Scrooling, so then you will be able   to do it.
$$\:{With}\:{patience}\:{and}\:{persistance}.\: \\ $$$$\:{Click}\:{on}\:{the}\:{left}\:{side}\:{menu},\:{select}\:{Inserct}\:{Drawing}, \\ $$$$\:{then}\:{you}\:{really}\:{have}\:{to}\:{figure}\:{out}\:{how}\:{it}\:{all}\:{works}. \\ $$$$\:{It}'{s}\:{really}\:{quite}\:{a}\:{torture}. \\ $$$$\:{I}\:{woudn}'{t}\:{recomend}\:{doing}\:{this},\:{unless}\:{you}\:{are} \\ $$$$\:{a}\:{person}\:{with}\:{iron}\:{made}\:{nervse}\:{like}\:{I}\:{am}.\: \\ $$$$\: \\ $$$$\:{P}.{S}.\:{If}\:{anyway}\:{you}\:{try}.\:{To}\:{get}\:{out}\:{from}\:{drawing} \\ $$$$\:{creation},\:{open}\:{again}\:{left}\:{menu}\:{and}\:{select}\: \\ $$$$\:{Enable}\:{Vertical}\:{Scrooling},\:{so}\:{then}\:{you}\:{will}\:{be}\:{able} \\ $$$$\:{to}\:{do}\:{it}. \\ $$
Commented by fantastic2 last updated on 22/Nov/25
i tried this before you.  3rd degree torture  anyway thanks for your time
$${i}\:{tried}\:{this}\:{before}\:{you}. \\ $$$$\mathrm{3}{rd}\:{degree}\:{torture} \\ $$$${anyway}\:{thanks}\:{for}\:{your}\:{time} \\ $$
Commented by mr W last updated on 22/Nov/25
have no understanding for such  self−torture. this app is made to  make equations, not to make   drawings.
$${have}\:{no}\:{understanding}\:{for}\:{such} \\ $$$${self}−{torture}.\:{this}\:{app}\:{is}\:{made}\:{to} \\ $$$${make}\:{equations},\:{not}\:{to}\:{make}\: \\ $$$${drawings}. \\ $$
Commented by fantastic2 last updated on 22/Nov/25
i know. thats why i use other  application or pen &paper
$${i}\:{know}.\:{thats}\:{why}\:{i}\:{use}\:{other} \\ $$$${application}\:{or}\:{pen}\:\&{paper} \\ $$

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