NCERT Solutions for Class 9 Maths Chapter 6: Lines and Angles

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    Q. In the given figure, if lines PQ and RS intersect at a point T such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°. Find ∠SQT.

    ntersect

    Ans. Given : ∠P = 95°, ∠R = 40° and ∠S = 75°
    In DPRT,
    ∠P + ∠R + ∠PTR = 180°
    ⇒ ∠PTR = 180° – ∠P – ∠R
    ⇒ ∠PTR = 180° – 95° – 40°
    ⇒ ∠PTR = 45°
    ... ∠STQ = ∠PTR = 45°
    (Vertically opposite angle)
    In DSTQ,
    ∠Q + ∠S + ∠STQ = 180°
    ⇒ ∠SQT + 75° + 45° = 180°
    ⇒ ∠SQT = 180° – 120°
    = 60°
    ∠SQT = 60°

    Q. In the given figure, POQ is a line. Ray OR is perpendicular to PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2
    (∠QOS – ∠POS).

    perpendicular

    Ans. $$\\ Given : PQ\bot OR\\ To prove : ∠ROS =\frac{1}{2}(∠QOS – ∠POS)\\ Proof : ∠QOS = ∠ROS + ∠QOR\\ ∠POS = ∠POR – ∠ROS\\ \frac{(–)(–)+}{∠QOS – ∠POS = ∠QOR – ∠POR + 2 ∠ROS}\\ ⇒ ∠QOS – ∠POS = 90° – 90° + 2 ∠ROS\\ \ ∠ROS =\frac{1}{2} (∠QOS – ∠POS)$$

    Q. If two lines are intersect, then the vertically opposite angles are equal.

    Ans. If two lines are intersect, then the vertically opposite angles are equal.

    Q. In the given figure, PQ ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65°, then find the value of x and y.

    perpendiculars

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