Q25 of 93 Page 6

What value of x would make AOB a line in the figure, if ∠ AOC=4x and ∠ BOC=6x+30° ?
        

 ∠ AOC = 4x (given)∠ BOC = 6x+30° (Given)∠ AOC + ∠ BOC = 4x + (6x+30° ) = 180° (Linear pair axiom)⇒ 10x + 30° = 180°        ⇒ 10x = 180° - 30°                  = 150°             \\ x = 15°∴ The value of x = 15°.

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23 A transversal intersects two given lines in such a way that the interior angles on the same side of the transversal are equal. Show by means of a figure that the lines need not be parallel. State the condition under which the two lines will be parallel.
 24 OP bisects  ∠AOC, OQ bisects ∠COB  and OP ⊥ OQ. Show that A, O, B are collinear.
    
   26 If two lines are intersected by a transversal in such a way that the bisectors of a pair of corresponding angles are parallel, show that two lines are parallel. 27 In the figure, AB and CD are parallel lines. The bisectors of the interior angles on the same side of the transversal EF intersect at P. Prove that ∠GPH = 90°.