Q. 74.2( 5 Votes )
Given: ∆ABC is equilateral triangle.
To prove: ∠CAD = ∠CBE = ∠BCL
Let our triangle be ∆ABC, which is equilateral triangle as shown in the figure.
Hence all angles are equal and measure 60° each.
∴ ∠CAB = ∠CBA = ∠BCA = 60° …(1)
Also here, ∠CAD and ∠CBE are exterior angles of the triangle.
So, we know that,
∠CAB +∠CAD = 180° … exterior angle theorem
∠CBA + ∠CBE = 180° … exterior angle theorem
∠BCA + ∠BCL = 180° … exterior angle theorem
From (1) and above statements, we state that,
60° +∠CAD = 180°
60° + ∠CBE = 180°
60° + ∠BCL = 180°
Simplifying above statements,
∠CAD = 180° - 60° = 120°
∠CBE = 180° - 60° = 120°
∠BCL = 180° - 60° = 120°
Hence, the measure of each exterior angle of an equilateral triangle is 120°
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