In a triangle ∠ABC, ∠A =50°, ∠B =60° and ∠C = 70°. Find the measure of the angles of the triangle formed by joining the mid-points of the sides of this triangle.
Answers
The measure of the angles are 50°,60°,70°
Step-by-step explanation:
Lets consider D,E,F are the midpoints of BC,CA, and AB respectively.
∴ BC ║ FE, ED║ AB, DF ║CA
Transversal CB and CA intersect them at D and E respectively.
∴ ∠CDE = ∠B =60°
Similarly, ∠CED=∠A= 50°
∠AEF=∠C=70°
∠AFE=∠B=60°
DF ║ CA
∴∠BDF=∠C=70°
∠BFD =∠A=50°
Given BC is a straight line,
∴∠BDF+∠FDE+∠EDC = 180°
70°+∠FDE+60°=180°
∴∠FDE = 180°-130° = 50°
Similarly , ∠DEF =60° and ∠EFD = 70°
Hence the angles are 50°, 60°, 70°
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