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mathstudent55
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
InesWalston

Answer-

[tex]\boxed{\boxed{m\angle BCA=60^{\circ}}}[/tex]

Solution-

Given here,

  • [tex]AB||CD[/tex]
  • [tex]BC||DE[/tex]
  • [tex]m\angle DCE=70^{\circ}[/tex]
  • [tex]m\angle EDC =50^{\circ}[/tex]

As [tex]BC||DE[/tex], and DC is the transversal, so

[tex]\Rightarrow \angle EDC=\angle DCB\ \ \ (\because \text{Alternate Interior Angle})[/tex]

[tex]\Rightarrow m\angle DCB=50^{\circ}[/tex]

Ans also [tex]\angle DCE,\ \angle DCB,\ \angle BCA[/tex] are complementary angles. So

[tex]\Rightarrow m\angle DCE+ m\angle DCB+m\angle BCA=180^{\circ}[/tex]

[tex]\Rightarrow m\angle BCA=180^{\circ}-m\angle DCE-m\angle DCB[/tex]

[tex]\Rightarrow m\angle BCA=180^{\circ}-70^{\circ}-50^{\circ}=60^{\circ}[/tex]

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