Question

3)
In the given figure, AB || CD, angleEAB = 105°, angleAEC = 25° and angleECD =
xº. Find the value of x.​

Answer 1

Answer:

x = 130˚

Step-by-step explanation:

Extend DC till it intersects AE at a point P.

So, angleCPE = angleBAE                      [Corresponding angles]

                       = 105˚

In ∆PCE,

anglePCE + anglePEC + angle EPC = 180˚             [Sum of all angles in ∆ = 180˚]

anglePCE +      25˚       +     105˚        = 180˚

                                  anglePCE        = 50˚

Now, angleDCE + anglePCE = 180˚        [Linear pair]

                  x       +   50˚          = 180˚

                                         x    = 130˚

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