Question

answer the ques in the attachment​

Answer 1

Answer:

Angle BAE = 45°

Angle CAD = 45°

Answer 2

Question :-

2. In the above figure ,

What are the respective measures

of ∠BAE and ∠CAD ?

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Solution :-

First I am solving ∠BAE ,

Now , see all the angles properly I wrote .

So, first we have to find out the value of ∠ABE . let's Find out :-

⟹∠ABE + ∠FBA = 180 ° [Linear pair].

∠FBA is already given that is 130°.

⟹ ∠ABE + 130° = 180 °

⟹ ∠ABE = 180° - 130°

⟹ ∠ABE = 50° .

Now , can you notice a triangle With ∠ABE .

∠ABE = 50°

∠AEB = 85° [Given]

So, let's find out ∠BAE

∠ABE + ∠AEB + ∠BAE = 180° [Sum of three angles of a triangle is 180°]

⟹ 50° + 85° + ∠BAE = 180°

⟹ 135° + ∠BAE = 180°

⟹ ∠BAE = 180° - 135°

⟹ ∠BAE = 45°.

∴ ∠BAE is 45°.

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Secondly I am solving for ∠CAD ,

Here, first finding out ∠DAE

AD = AE

Therefore , we can also say

∠AED = ∠ADE = 85 ° [Opposite angles are equal]

In triangle ADE ,

∠ADE + ∠AED + ∠DAE = 180° [Sum of three angles of a triangle is 180°]

⟹ 85° + 85° + ∠DAE = 180°

⟹ 170° + ∠DAE = 180°

⟹ ∠DAE = 180° - 170°

⟹ ∠DAE = 10° .(Equation 1) ⋆

Now, let's find ∠AEC

In triangle AEC ,

∠AEC + ∠AED = 180° [Linear pair].

∠AED is already given 85°

⟹∠AEC + 85° = 180°

⟹ ∠AEC = 180° - 85°

⟹ ∠AEC = 95° .

Now, Finding ∠EAC ,

∠ACE = 50° (Given)

∠ACE + ∠EAC + ∠AEC = 180° [Sum of three angles of a triangle is 180°]

⟹ 95° + 50° + ∠EAC = 180°

⟹ 145° + ∠EAC = 180°

⟹ ∠EAC = 180° - 145°

⟹∠EAC = 35° . (Equation 2) ⋆

∴ ∠CAD = ∠DAE + ∠EAC

From Equation 1 and Equation 2 ,

∠CAD = ∠DAE + ∠EAC

⟹∠CAD = 10 + 35

⟹ 45 = 10 + 35

∴ ∠CAD = 45°.

$\tt{ \huge \therefore} \bf \underline{\: \: \angle \: BAE = 45° \: \: \: \angle CAD = 45°} \star$

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