Plzzzz help..........

1.	Plzzzz help..........
Answer» 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){\<klux>LINE</klux>(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 . $\bf Now\:\:,$ $\tt:\implies \angle CEG + \angle GED = 180^{\circ}$ $\tt:\implies \angle CEG + 126^{\circ}=180^{\circ}$ $\tt:\implies \angle CEG =\lgroup 180^{\circ}-126^{\circ}\rgroup$ $\tt:\implies \angle CEG = 54^{\circ}$ $\underline{\boxed{\red{\tt\longmapsto \angle FGE = 54^{\circ}}}}$ $\pink{\qquad\qquad\qquad\bf Hence,}$ $\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:AGE\:=\:126^{\circ}}}$ $\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:GEF\:=\:36^{\circ}}}$ $\boxed{\pink{\bullet}\:\:\green{\sf Value\:of\:\angle\:FGE\:=\:54^{\circ}}}$

Answer»

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){\<klux>LINE</klux>(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 .

$\bf Now\:\:,$