Question

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC=
A. 94°
B. 54°
C. 40°
D. 44°

Answer 1

Answer:

option C

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Answer 2

Given: The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°.  

 

To Find : ∠BAC

 

Proof :

From figure , ∠ABD = 94°  and ∠ACE = 126°.

∠ABD + ∠ABC = 180°

[Linear pair]

94° + ∠ABC  = 180°

∠ABC = 180° - 94°

∠ABC = 86° ……………(1)

 

∠ACE + ∠ACB = 180°  

[Linear pair]

126° + ∠ACB = 180°  

∠ACB = 180°  - 126°

∠ACB = 54° …………... (2)

 

In ∆ABC,

Since Sum of the angles of a triangle is 180° :  

∠ABC + ∠ACB + ∠BAC = 180°  

86°  + 54°  + ∠BAC = 180°

[From eq 1 & 2]

140° + ∠BAC = 180°

∠BAC = 180° - 140°

∠BAC = 40°

Hence the measure of ∠BAC is 40°.

Among the given options option (C) 40° is correct.

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B. x = 50°, y = 45°

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