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8th Class Mathematics Practical Geometry Question Bank Geometry

  • question_answer
    AB is a diameter of a circle with centre O and radius OD is perpendicular to AB. If C is any point on arc DB, then the measures of \[\angle 4=\angle 2\] and \[\angle 6=\angle 3\] will be

    A)  \[\angle 1=\angle 2\]              

    B)  \[\angle 3=\angle 5\]

    C)  \[{{180}^{o}}\]          

    D)  \[\angle 1+\angle 3={{180}^{o}}\]

    Correct Answer: C

    Solution :

    \[{{80}^{o}}\]    (\[{{100}^{o}}\] Angle in semi-circle is\[90{}^\circ \]) Since,   \[\angle DAC={{54}^{o}}\] \[\angle ACB={{63}^{o}}\] \[\angle BAC\]   (Half of angle\[{{72}^{o}}\]) Now,  \[{{54}^{o}}\]   (Linear pair) Consider \[{{27}^{o}}\] \[{{90}^{o}}\] \[\angle BOD={{120}^{o}}\] \[\angle ACD\] \[{{30}^{o}}\]\[{{40}^{o}}\] \[{{60}^{o}}\] \[{{90}^{o}}\] Now, \[{{30}^{o}}\] \[{{45}^{o}}\]  \[{{60}^{o}}\]   (Sum of angles of\[{{75}^{o}}\]) Now, \[\angle CAD={{50}^{o}}\] (\[\angle BED={{120}^{o}}\] Angles on same arc AD)       


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