Question

In the given figure, AB = AC and ACD = 120°, then find BAC. ​

Answer 1

ǫᴜᴇsᴛɪᴏɴ →

In the given figure, AB = AC and ACD = 120°, then find BAC

ᴀɴsᴡᴇʀ →

$\longmapsto\tt{∵AB=AC⇒∠ABC=∠ACB=x(say)}$

Let

$\longmapsto\tt{∠BAC=y}$

We know,

Exterior angles = sun of interior opposite angles

$\longmapsto\tt{or, 120° = ∠ABC+∠BAC}$

$\longmapsto\tt{or, 120° = x+y−−−(1)}$

Again,

$\longmapsto\tt{∠ACB+∠ACD=180°}$

$\longmapsto\tt{or, x+120° = 180° }$

$\longmapsto\tt\boxed{x = 60°}$

$\longmapsto\tt{From (1), 60° + y = 120°}$

$\longmapsto\tt\boxed{y = 60°}$

$\longmapsto\tt\boxed{∠A = 60°}$