Question

In the figure below ab and and cd are parallell compute all the angles in the figure

Answer 1

Since AB//CD ,

       ∠ECD = ∠CAB = 70°

       ∠EDC = ∠DAB = 60°

       ∠ACD = 180° - ∠CAB = 180° - 70° = 110°

       ∠CDB = 180° - ∠ABD = 180° - 60° = 120°

In Δ CDE , ∠C + ∠D + ∠E =180°

                  ∠E = 180° - (70 + 60)° = 180° - 130° = 50°

Answer 2

All the angles in the figure are,

∠ AEB = 50°, ∠ ECB = 70°, ∠ EDC = 60°, ∠ DCA = 110°, ∠ CDB = 120°.

Given: In the figure given, AB || CD.

To Find: Compute all the angles in the figure.

Solution:

We can solve the numerical by applying the formula of parallel lines and the concept of total angles in a triangle.

We are given that,

∠ EAB = 70° and ∠ EBA = 60°

So, we can say that,

   ∠ AEB + ∠ EAB + ∠ EBA = 180°                      [Total angles in a triangle]

⇒ ∠ AEB +  70° +  60° = 180°

⇒ ∠ AEB = 180° - 130°

               = 50°

We know that AB || CD, so we can say that,

    ∠ EAB = ∠ ECB                            [ Corresponding angles ]

∴   ∠ ECB = 70°

Again, ∠ EBA = ∠ EDC                      [ Corresponding angles ]

∴   ∠ EDC = 60°

Now, ∠ DCA = 180° - 70°                  [ Angles on a straight line ]

                     = 110°

again, ∠ CDB = 180° - 60°                 [ Angles on a straight line ]

                       = 120°

Hence, compiling the answer we get;

All the angles in the figure are,

∠ AEB = 50°, ∠ ECB = 70°, ∠ EDC = 60°, ∠ DCA = 110°, ∠ CDB = 120°.

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