Lines a and b are parallel. line c is a transversal. find the measures of all angles formed by a, b, and c, one of the angles is 70° bigger than the other

Angles are either 55° or 125°.

Step-by-step explanation:

See the attached diagram.

Let aa' and bb' are two parallel straight lines and cc' is a transversal that meets aa' at o and bb' at o' points.

Now, ∠coa' + ∠coa =180° ..... (1)

Assume by the condition given ∠coa' = x and ∠coa = x+70

Hence, from equation (1), 2x + 70 = 180

⇒ x = 55°

Then ∠coa' =55° and ∠coa = 70+55 = 125°

So, ∠o'oa' = 125° as ∠coa = ∠ o'oa' {Opposite angles}

Again, ∠aoo' = 55° as ∠coa' = ∠aoo' {Opposite angles}

Now, ∠coa' = ∠oo'b' {Corresponding angles} = 55°

and ∠bo'c' = ∠oo'b' = 55° {Opposite angles}

Again ∠oo'b = ∠coa = 125° {Corresponding angles}

and ∠b'o'c' = ∠oo'b =125° {Opposite angles}

(Answer)

The 4 angles formed in each case are: , , and .

Step-by-step explanation:

Line c being transversal implies that it forms 4 angles with lines a and b individually of which 2 in each case are opposite angles, thus are equal.

Let one of the angles be represented by , but the other is greater by , so that =  ( + )

Thus, we have;

    + + ( + ) + ( + ) =    ( the sum of angles at a point)

      + + + + + =

 +   =

= -

=

Divide both sides by 4,

=

The other angle is calculated thus,

   ( + ) = +

                 =

Thus the 4 angles formed in both cases have the values; , , and .

answer is x<