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arsen [322]
2 years ago
8

Find the m∠BCA, if m∠DCE = 70° and m∠EDC = 50°. 50° 60° 70° 80°

Mathematics
2 answers:
lara [203]2 years ago
5 0
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
NemiM [27]2 years ago
5 0

<u>Answer-</u>

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

<u>Solution-</u>

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}

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