Q38 of 93 Page 6

In the figure, if l || m, find the value of x. 

Since l || m and DC is the transversal
... ∠D + ∠1 = 180°        ............................(i)
⇒ 60° + ∠1 = 180° ⇒ ∠1 = 120°  ..............(ii)
     Now ∠2 = ∠1 = 120°    (Vertically opposite angles)...................... (iii)
In Δ ABC, we have ∠A + ∠B + ∠C = 180°
                  ⇒ 25° + x° + 120° = 180°
           ⇒ x = 180° - 120° - 25° = 35°

More from this chapter

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36 One of the four angles formed by two intersecting lines is a right angle. Show that the other three angles will also be right angles. 37 If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle. 39 AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠ BOD. If ∠ BOF=35° , find ∠ BOC and ∠ AOD. 40 Sides BC, BA and CA of ∠ABC are produced to D, F and E respectively. If ∠ACD = 120° and ∠EAF = 45°,  find three angles of ∠ABC.