Question

Find the m∠DEC, if m∠BAC = 50° and m∠CBA = 70°

Answer 1

the m∠DEC=60°

Explanation:

As given, information the triangle is shown in figure-1

Given:

m∠BAC = 50°

m∠CBA = 70°

we need to find m∠DEC

Since, sum of interior angles of triangle is 180°.

In triangle ABC,

m∠BAC+m∠CBA+m∠ACB=180°

50° + 70° + m∠ACB =180°

120° + m∠ACB =180°

subtract 120° from both the sides in above,

m∠ACB =180° - 120°

m∠ACB =160°

from the figure, we can see that BC║DE,

therefore

m∠DEC=m∠ACB

m∠DEC=60°

Therefore, the m∠DEC=60°

Answer 2

the complete question in the attached figure
we know that
m∠BAC = 50°
m∠CBA = 70°
and
m∠BAC+m∠CBA+m∠ACB=180°
then
m∠ACB=180-[m∠BAC+m∠CBA]---------> 180°-[50°+70°]=60°
m∠ACB=60°
remember that
BC║DE
therefore
m∠ACB=m∠DEC
m∠DEC=60°

the answer is m∠DEC=60°