Question

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.

Answer 1

since the triangles are similar

angle DEC = 60 degrees

3 angles inside a triangle equal 180 degrees

BAC = DCE = 64

CBA = EDC = 56

DEC = 180 -56 -64 = 60 degrees

used angle-angle theorem

Answer 2

$\text{Answer: }\angle DEC=60\textdegree$

Explanation:

Since we have given that

m∠BAC = 64° and m∠CBA = 56°

and AB║CD and BC║DE

First, we consider Δ ABC,

As we know two angles of a triangle so we need to find the third angle, for which we'll use the "Angle Sum Property",

Angle Sum Property, states that the sum of three angles of a triangle is  $180\textdegree$

Now, we will apply this,

$\angle BAC+\angle ABC+\angle ACB=180\textdegree\\\\64\textdegree+56\textdegree+\angle ACB=180\textdegree\\\\120\textdegree+\angle ACB=180\textdegree\\\\\angle ACB=180\textdegree-120\textdegree\\\\\angle ACB=60\textdegree$

Now, as we have given that

BC║DE

so,

m∠ACB=m∠DEC

(∵ Corresponding angles are equal for given parallel lines)

So,

$\angle ACB=\angle DEC=60\textdegree$