Question

In the Diagram below DE≅AE ,BA∥CE
, CB∥DA
and m∠C=65∘

Find m∠BAE

Answer 1

∠ DAE = 130°

Explanation:

ABCD is a parallelogram ( opposite sides are parallel )

The opposite angles of a parallelogram are congruent , then

∠ BAD = ∠ BCD = 65°

∠ ADE = ∠ BAD = 65° ( alternate angles )

Since DE = AE then Δ ADE is isosceles with 2 base angles congruent, that is

∠ DAE = ∠ ADE = 65°

Then

∠ BAE = ∠ BAD + ∠ DAE = 65° + 65° = 130°