Math, asked by faQq, 4 months ago

plzzzz help.......... ​

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Answered by BrainlyEmpire
125

ɢɪᴠᴇɴ :-

Measure of ∠FED = 90° .

AB is parallel to CD i.e. AB || CD .

Measure of ∠GED = 126°

ᴛᴏ ғɪɴᴅ:-

The values of ∠AGE , ∠GEF & ∠FGE .

ᴀɴsᴡᴇʀ :-

\underline{\textsf{\textbf{\purple{\red{$\leadsto$} Figure :- }}}}

\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\put(1,0){\vector(-1,0){1}}\put(2,0){\vector(1,0){2}}\put(1,0){\line(1,0){1}}\put(3,0){\line(-1,2){2}}\put(1,4){\vector(-1,0){1}}\put(2,4){\vector(1,0){2}}\put(1,4){\line(1,0){1}}\put(3,4){\line(0,-1){4}}\put(2.9,0.5){ $90^{\circ}$}\put(1,4.5){$\tt C$}\put(0,4.5){$\tt A$} \put(3,4.5){$ \tt F $}\put(4,4.5){$\tt B $}\put(0,-0.5){$\tt C $}\put(3,-0.5){$\tt E $}\put(4,-0.5){$\tt D $}\put(3.3,1){ $ 126^{\circ}$}\put(3.2,0){\line(0,1){0.2}}\put(3.2,0.2){\line(-1,0){0.2}}\qbezier(3.8,0)(4.5,0.8)(2.3,1.3)\end{picture}

\tt As\:per\: data\: given\:in\: Question:-

\blue{\sf \angle FED = 90^{\circ}}

\blue{\sf \angle GED = 126^{\circ}}

\green{\sf Before\:we\:procced\:we\:must\:know:-}

Alternate Interior angles are equal.

Sum of co - interior angles is 180° .

Alternate exterior angles are equal.

The measure of straight line is 180°.

\red{\underbrace{\underline{\textsf{\textbf{\purple{\red{$\dag$} For\: finding\:\:$\angle$\: AGE :}}}}}}

Since here AB || CD , so ∠AGE and ∠GED are co-interior angles . Hence they will be equal .

So , \red{\bf \angle AGE = 126^{\circ}}

___________________________________

\red{\underbrace{\underline{\textsf{\textbf{\purple{\red{$\dag$} For\: finding\:\:$\angle$\: GEF :}}}}}}

\tt Here\:we\:can\:see\: that:-

\tt:\implies\angle GED = 126^{\circ}

\tt:\implies \angle GEF + \angle FED = 126^{\circ}

\tt:\implies \angle GEF + 90^{\circ}=126^{\circ}

\tt:\implies \angle GEF = 126^{\circ}-90^{\circ}

\underline{\boxed{\red{\tt\longmapsto \angle GEF = 36^{\circ}}}}

___________________________________

\red{\underbrace{\underline{\textsf{\textbf{\purple{\red{$\dag$} For\: finding\:\:$\angle$\: FGE :}}}}}}

Firstly let's find ∠ CEG , since ∠ FGE and ∠CEG are alternate interior angles , So they will be equal . Hence we can subsitute ∠ FGE in place of ∠CEG .

\bf Now\:\:,

\tt:\implies \angle CEG + \angle GED = 180^{\circ}

\tt:\implies \angle CEG + 126^{\circ}=180^{\circ}

\tt:\implies \angle CEG  =\lgroup 180^{\circ}-126^{\circ}\rgroup

\tt:\implies \angle CEG = 54^{\circ}

\underline{\boxed{\red{\tt\longmapsto \angle FGE  = 54^{\circ}}}}

\pink{\qquad\qquad\qquad\bf  Hence,}

\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:AGE\:=\:126^{\circ}}}

\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:GEF\:=\:36^{\circ}}}

\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:FGE\:=\:54^{\circ}}}

Answered by Anonymous
1

Answer:

Given :-

AB || CD ,EF ⊥ CD

∠GED = 126°

Find :-

GEF , FGE and AGE

Solution :-

Diagram :-

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1. ∠AGE = ∠GED = 126∘ [alternate interior angles]

  •   ∠GED = ∠GEF + ∠FED = 126°

2. ∠GEF + 90° = 126°

  • ∠GEF = 126° − 90°

  • = 36° { By EF⊥CD }

  • ∠GEF = 36°

3. ∠CEG + ∠GED = 180°

As from the given

  • ∠CEG + 126° = 180° { By linear pair Axiom }

  • ∠CEG = 180° − 126°
  • ∠CEG = 54°
  • ∠FGE = ∠CEG = 54°  { By Alternate int. angles }

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