Question

Find the m∠BCA, if m∠DCE = 70° and m∠EDC = 50°.

50°
60°
70°
80°

Answer 1

Because of the parallel lines, angles A and DCE are congruent.
Also, angles E and BCA are congruent.
That makes angles B and D congruent.

m<DCE = 70 and m<EDC = 50, so m<E = 60

m<BCA = m<E = 60

Answer 2

Answer-

$\boxed{\boxed{m\angle BCA=60^{\circ}}}$

Solution-

Given here,

• $AB||CD$
• $BC||DE$
• $m\angle DCE=70^{\circ}$
• $m\angle EDC =50^{\circ}$

As $BC||DE$, and DC is the transversal, so

$\Rightarrow \angle EDC=\angle DCB\ \ \ (\because \text{Alternate Interior Angle})$

$\Rightarrow m\angle DCB=50^{\circ}$

Ans also $\angle DCE,\ \angle DCB,\ \angle BCA$ are complementary angles. So

$\Rightarrow m\angle DCE+ m\angle DCB+m\angle BCA=180^{\circ}$

$\Rightarrow m\angle BCA=180^{\circ}-m\angle DCE-m\angle DCB$

$\Rightarrow m\angle BCA=180^{\circ}-70^{\circ}-50^{\circ}=60^{\circ}$