Respuesta :

Will recommend to keep in touch with attached picture while reading Answer as names of angles are written according to attached picture!

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[tex] \rm\angle BAO = \angle DCO[/tex]

Reason:-

Alternate Interior Angles.

What is Alternate Interior Angles.?

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

Remember this only possible as lines are parallel give. We get to know that lines are parallel as upward arrow is marked in that lines.

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[tex] \rm \therefore\angle DCO = 2a \degree[/tex]

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Now Let's find angle DOC.

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[tex] \rm\angle DOC +\angle DOA = 180\degree[/tex]

Reason:-

LP (Linear Pair)

What is LP (Linear Pair) ?

Linear pair of angles are formed when two lines intersect each other at a single point

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So let's solve:-

[tex] \hookrightarrow \rm\angle DOC +\angle DOA = 180\degree[/tex]

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[tex] \hookrightarrow \rm78 \degree +\angle DOC= 180\degree[/tex]

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[tex] \hookrightarrow \rm\angle DOC = 180\degree - 78 \degree [/tex]

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[tex] \hookrightarrow \rm\angle DOC =102\degree [/tex]

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Finally Let's find value of a.

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[tex] \rm\angle CDO + \angle DCO + \angle DOC = 180° \\ [/tex]

reason:-

Sum of angles triangle = 180°

Formula to find :

  • (number of angles - 2) × 180°
  • (3 - 2) × 80°
  • 1 × 180°
  • 180°

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So let's find:-

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[tex] \dashrightarrow \rm\angle CDO + \angle DCO + \angle DOC = 180° \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \rm2a + a+ 102= 180° \\ [/tex]

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[tex] \dashrightarrow \rm3 a+ 102= 180° \\ [/tex]

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[tex] \dashrightarrow \rm3 a= 180° - 102\\ [/tex]

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[tex] \dashrightarrow \rm3 a= 78° \\ [/tex]

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[tex] \dashrightarrow \rm a= 78° \div 3 \\ [/tex]

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[tex] \dashrightarrow \bf a= 26°\\ [/tex]

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Now Let's find angle b

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angle b = angle a

Reason:-

Alternate Interior Angles.

Therefore angle b = 26°

Ver imagen WindyMint

The unknown angles formed when the two transversal cuts the parallel lines are 26°, 26° and 52°.

Angles formed when transversals line cuts parallel lines.

When two or more lines are cut by a transversal, the angles formed includes corresponding angles, alternate angles etc.

Therefore,

a = b (alternate angles)

Hence,

2a + b + (180 - 78) = 180 (sum of angles in a triangle)

2a + a + 102 = 180

3a + 102 = 180

3a = 180 - 102

3a = 78

a = 78 / 3

a = 26

Therefore, the unknown angles are 26°, 26°, and 2(26) = 52°

learn more on angles here: https://brainly.com/question/26666371

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