Question

plzzzz help.......... ​

Answer 1

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 :-

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

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

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

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

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

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 2

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 }