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Question
In a triangle ∠ABC, ∠A = 50°, ∠B = 60° and ∠C = 70°. Find the measures of the angles of
the triangle formed by joining the mid-points of the sides of this triangle.
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Solution
In ΔABC
D and E are midpoints of AB and BC
By midpoint theorem
∴ DE || AC, DE = `1/2` AC.
F is the midpoint of AC
Then, DE = `1/2` AC = CF
In a quadrilateral DECF
DE || AC, DE = CF
Hence DECF is a parallelogram
∴`∠`C = `∠`D = 70° [Opposite sides of parallelogram]
Similarly
BEFD is a parallelogram, `∠`B = `∠`F = 60°
ADEF is a parallelogram, `∠`A = `∠`E = 50°
∴Angles of ΔDEF
`∠`D = 70°, `∠`E = 50°, `∠`F = 60°
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