# Class 9 Lines and Angles Important Questions

Important Questions**Lines and Angles Important Questions**

**The diagonals of the rectangle ABCD intersect at O. If ∠COD = 78°, then ∠OAB is:****35**^{o}**51**^{o}**70**^{o}**110**^{o}

**If AB =***x*+ 3, BC = 2*x*and AC = 4*x*– 5, then for what value of ‘*x*’, B lies on AC?**2****3****5****8**

**In the given Figure , POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2(∠ QOS – ∠ POS).****In the given Figure, if PQ || RS, ∠ MXQ = 135° and ∠ MYR = 40°, find ∠XMY.****Prove that the angle formed by the bisector of interior angle A and the bisector of exterior angle B of a triangle ABC is half of angle C.****In the given Figure, the sides AB and AC of ∆ABC are produced to points E and D respectively. If bisectors BO and CO of ∠ CBE and ∠ BCD respectively meet at point O, then prove that ∠BOC = 90° – 1/2 ∠BAC.****Bisectors of interior ∠B and exterior ∠ACD of a Δ ABC intersect at the point T.Prove that ∠ BTC = ½ ∠ BAC.****A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.****In the figure, PS is the bisector of ∠QPR and PT ⊥ QR. Show that ∠TPS = ½(∠Q – ∠R).****If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle.****The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find all the three angles.****The exterior angles obtained on producing the base of a triangle both ways are 100° and 120°. Find all the angles of the triangle.**

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