Q43 of 93 Page 6

In the figure AB || CD and ∠ECD = 100° and ∠ABE = 110°, find the value of x.

Since AB || CD
    ... AF || CD ….(AB was produced to F) and CF is transversal 
... ∠DCF = ∠BFC = 100°
Now ∠BFC + ∠BFE = 180° ….(Linear pair)
   ... 100° + ∠BFE = 180°
              ... ∠BFE = 180° - 100° = 80°
Now in ΔBFE, we have
  ∠ABE = ∠BFE +∠BEF
⇒ 110° = 80° + x°
    Þ x = 110° - 80° = 30°

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41 Which of the following statements are true (T) and which are false (F)? Give reasons.
        (i) Angles forming linear pair are supplementary.
        (ii) If two adjacent angles are equal, then each angle measures 90°.
        (iii) Angles forming a linear pair can both be acute angles.
        (iv) Two distinct lines in a plane can have two points in common.
        (v) If angles forming a linear pair are equal, then each of these angles is of measure 90°.
       (vi) If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.
       (vii) If two lines intersect and one of the angles so formed is a right angle, then the other three angles will not be right angles. 42 Fill in the blanks so as to make the following statements true:
(i) Two distinct points in a plane determine a …………… line. (ii) Two distinct……….. in a plane cannot have more than one point in common. (iii) Given a line and a point, not on the line, there is one and only …………. line which passes through the given point and       is …….. to the given line.
(iv) A line separates a plane into ………….. parts namely the two ……… and the …………. itself.
(v) If one angle of a linear pair is acute, then its other angle will be ………..
(vi) If a ray stands on a line, then the sum of the two adjacent angles so formed is ………..
(vii) If the sum of two adjacent angles is 180°, then the ……….. arms of the two angles are opposite rays.
(viii) If two lines intersect, then vertically opposite angles are ………… 44 In the given figure, p is a transversal to lines m and n, ∠ 2 = 120° and ∠ 5 = 60° . Prove that m || n.
               45 The side BC of a triangle ABC is produced, such that D is on ray BC. The bisector of ∠A meets BC at E. Show that ∠ABC + ∠ACD = 2 ∠AEC.