Question

Proof that angle BAC =72 degree​

Answer 1

Answer:

hope it will help you

Step-by-step explanation:

In ΔABC, we have

∠B=

2∠C

or,

∠B=

2y

, where

∠C=

y

AD is the bisector of ∠BAC

. So, let

∠BAD=

∠CAD=

x

Let BP be the bisector of ∠ABC . Join PD.

In ΔBPC, we have

∠CBP=

∠BCP=

y⇒

BP=

PC

In

Δ ′

ABP and DCP, we have

∠ABP=

∠DCP

, we have

∠ABP=

∠DCP=

y

AB=

DC

[Given]

and,

BP=

PC

[As proved above]

So, by SAS congruence criterion, we obtain

ΔABP≅

ΔDCP

⇒

∠BAP=

∠CDP

and

AP=

DP

⇒

∠CDP=

2x

and

∠ADP=

DAP=

x

[∴

∠A=

2x]

In ΔABD, we have

∠ADC=

∠ABD+

∠BAD⇒

x+

2x=

2y+

x⇒

x=

y

In

ΔABC, we have

∠A+

∠B+

∠C=

180

∘

⇒

2x+

2y+

y=

180

∘

⇒

5x=

180

∘

[∵

x=

y]

⇒

x=

36

∘

Hence,

∠BAC=

2x=

72