Question

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In ∆ABC, <A= 60⁰, <B =70⁰and <C = 50⁰.Points D,E and F are the mid- points of the

sides BC, AC and AB respectively. Find the measures of the angles of the triangle formed

by joining the midpoints of the sides of ∆ ABC​

Answer 1

Answer:

Step-by-step explanation:

In ∆ABC, D and E are midpoints of AB and BC  By midpoint theorem

Therefore 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

Therefore angle C = angle D =70 degree

(Opposite sides of a parallelogram)

Similarly,

BEFD is a parallelogram, angle B=angle F=60 degree

ADEF is a parallelogram,  angle A= angle E=50 degree

Therefore angles of Triangle DEF are:

angle D=70 degree, angle E=50 degree and angle F=60 degree

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