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Licemer1 [7]
3 years ago
13

I need help ASAP. Thank you :)

Mathematics
1 answer:
kvasek [131]3 years ago
8 0

m∠FDE = 52°

Solution:

Given data:

DE ≅ DF, CD || BE, BC || FD and m∠ABF = 116°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠ABF + m∠CBF = 180°

116° + m∠CBF = 180°

m∠CBF = 64°

If CD || BE, then CD || BF.

Hence CD || BE and BE || FD.

Therefore BFCD is a parallelogam.

<em>In parallelogram, Adjacent angles form a linear pair.</em>

m∠CBF + m∠BFD = 180°

64° + m∠BFD = 180°

m∠BFD = 116°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠BFD + m∠DFE = 180°

116° + m∠DFE = 180°

m∠DFE = 64°

we know that DE ≅ DF.

<em>In triangle, angles opposite to equal sides are equal.</em>

m∠DFE = m∠DEF

m∠DEF = 64°

<em>sum of all the angles of a triangle = 180°</em>

m∠DFE + m∠DEF + m∠FDE = 180°

64° + 64° + m∠FDE = 180°

m∠FDE = 52°

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