Question

please answer me please ​

Answer 1

Answer:

54 is answer

Step-by-step explanation:

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Answer 2

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 .

$\bf Now\:\:,$

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

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

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

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

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

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

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

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

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