Question

DE=DF and <EDF=50°. find the values of a ,b and c​

Answer 1

Answer:

a = 130°, b = 65°,c = 115°

Step by step explanation:

Given

DE = DF

Angle EDF = 50°

To find

Value of a,b and c.

a = 180° - 50° ( linear pair)

a = 130°

Now, Since DE = DF (means that the ∆ is an Isosceles ∆)

According to Isosceles triangle theorem, Angles opposite to the equal sides are also equal,So

b = angle DFE. ...(i)

Now,

50° + b + angle DFE =180° (Angle sum property)

50° + b + b = 180° (from i )

2b = 180° - 50°

2b = 130°

b = 65°

c = 180° - 65° = 115°

Answer 2

$a \: + 50 = 180 (linear \: pair) \\ a = 130 \\ \\ \\ b = angle \: dfe \: (de = df) \\ b \: + angle \: dfe + 50 = 180(angle \: sum \: property) \\ \\ 2b + 50 = 180 \\ 2b = 130 \\ b = 65 \\ \\ angle \: dfe = 65 \\ angle \: dfe + c = 180 \\ 65 + c = 180 \\ c = 115$