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

`\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)`