ABC is an equilateral triangle. Its side BC is produced upto point E such that C is mid-point of BE. Calculate the measure of angles ACE and AEC.
ABC is an equilateral triangle. Its side BC is produced upto point E such that C is mid-point of BE. Calculate the measure of angles ACE and AEC.
We form our diagram from given information , As :
Here , AB = BC = CA as ABC is a equilateral triangle, Also given BC = CE ( As C is mid point of BE ) , Then
AB = BC = CA = CE
We know equilateral triangle all angles are at 60° .
So,
∠ ABC = ∠ ACB = ∠ BAC = 60° --- ( 1 )
And
∠ ACB + ∠ ACE = 180° , Substitute value from equation 1 we get
60° + ∠ ACE = 180°
∠ ACE = 120° --- ( 2 )
And triangle AEC is a isosceles triangle as side AC = CE so from base angle theorem we get
∠ AEC = ∠ EAC --- ( 3 )
From angle sum property of triangle we get in triangle AEC
∠ AEC + ∠ EAC + ∠ ACE = 180° , Substitute values from equation 2 and 3 and get
∠ AEC + ∠ AEC + 120° = 180°
2 ∠ AEC = 60°
∠ AEC = 30°
Therefore,
∠ ACE = 120° and ∠ AEC = 30° ( Ans)
We form our diagram from given information , As :
Here , AB = BC = CA as ABC is a equilateral triangle, Also given BC = CE ( As C is mid point of BE ) , Then
AB = BC = CA = CE
We know equilateral triangle all angles are at 60° .
So,
∠ ABC = ∠ ACB = ∠ BAC = 60° --- ( 1 )
And
∠ ACB + ∠ ACE = 180° , Substitute value from equation 1 we get
60° + ∠ ACE = 180°
∠ ACE = 120° --- ( 2 )
And triangle AEC is a isosceles triangle as side AC = CE so from base angle theorem we get
∠ AEC = ∠ EAC --- ( 3 )
From angle sum property of triangle we get in triangle AEC
∠ AEC + ∠ EAC + ∠ ACE = 180° , Substitute values from equation 2 and 3 and get
∠ AEC + ∠ AEC + 120° = 180°
2 ∠ AEC = 60°
∠ AEC = 30°
Therefore,
∠ ACE = 120° and ∠ AEC = 30° ( Ans)
