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Procedure : (i) Draw a circle of many ...

Procedure :
(i) Draw a circle of many radius with centre O.
(ii) Mark any four points A,B,C and D on the boundary. Make a cyclic quadrilateral ABCD and name the angles as in Fig. 1
(iii) Make a replica of the cyclic quadrilateral ABCD with the help of tracing paper
(iv) Make the cutout of the angles A,B,C and D as in Fig. 2
(v) Paste the angle cutout `angle1,angle2,angle3` and `angle4` adjacent to the angles opposite to A,B,C and D as in Fig . 3
Measure the angles `angle1+angle3`, and `angle2+angle4`.

Observe the Fig. 3 and complete the following :
`{:((i),angleA+angleC= . . . . . . . ,(ii),angleB+angleD =. . . . . . .),((iii),angleC+angleA= . . . . . . .,(iv),angleD+angleB= . . . . . . .):}`
2. Sum of opposite angles of a cyclic quadrilateral is . . . . . . . .
3. The opposite angles of a cyclic quadrilateral is . . . . . . .

Answer

Step by step text solution for Procedure : (i) Draw a circle of many radius with centre O. (ii) Mark any four points A,B,C and D on the boundary. Make a cyclic quadrilateral ABCD and name the angles as in Fig. 1 (iii) Make a replica of the cyclic quadrilateral ABCD with the help of tracing paper (iv) Make the cutout of the angles A,B,C and D as in Fig. 2 (v) Paste the angle cutout angle1,angle2,angle3 and angle4 adjacent to the angles opposite to A,B,C and D as in Fig . 3 Measure the angles angle1+angle3, and angle2+angle4. Observe the Fig. 3 and complete the following : {:((i),angleA+angleC= . . . . . . . ,(ii),angleB+angleD =. . . . . . .),((iii),angleC+angleA= . . . . . . .,(iv),angleD+angleB= . . . . . . .):} 2. Sum of opposite angles of a cyclic quadrilateral is . . . . . . . . 3. The opposite angles of a cyclic quadrilateral is . . . . . . . by MATHS experts to help you in doubts & scoring excellent marks in Class 9 exams.

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Knowledge Check

  • In a cyclic quadrilateral ABCD /_A=4x, /_C=2x the value of x is

    A
    `30^(@)`
    B
    `20^(@)`
    C
    `15^(@)`
    D
    `25^(@)`
  • In a cyclic quadrilaterals ABCD, angleA=4x, angleC=2x the value of x is

    A
    `30^(@)`
    B
    `20^(@)`
    C
    `15^(@)`
    D
    `25^(@)`
  • in a cyclic quadrilateral ABCD , cos A + cos B + cos C + cos d is

    A
    1
    B
    0
    C
    `pi`
    D
    2
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    In a cyclic quadrilaterals ABCD, angleA = 4x, angleC = 2x the value of x is

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