Respuesta :

jackiezhang2007

Answer and explanations:

since the triangle on the right is a right triangle, <CED is 70 degrees too and therefore <DCE is 40 degrees.

Then because of vertical angles, <ACB is also 40 degrees

<BAC is 180 degrees - 40 degrees - 70 degrees = 70 degrees.

Since there are 2 angles that have the same value, the triangle ABC is isosceles. Done!

mhanifa

Step-by-step explanation:

ΔCDE

  • CD = CE - given, therefore the triangle is isosceles
  • m∠CDE = 70° - given
  • m∠DEC = 70° - isosceles triangle has two equal angles opposite to equal sides
  • m∠DCE = 180° - 2*70° = 40° - sum of interior angles equals to 180°

ΔABC

  • m∠BCA = 40°- as vertical angle with ∠DCE
  • m∠ABC = 70° - given
  • m∠BAC = 180° - (70° + 40°) = 70° - sum of interior angles equals to 180°

m∠ABC = m∠BAC - the triangle has two equal angles, therefore has two equal sides and is isosceles

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