Question

3. In the given figure, if angleAOC + angleBOD = 242°,
find all the four angles​

Answer 1

Step-by-step explanation:⤵️

angle AOC = angle BOD

and

angle AOD = angle BOC

{vertically opposite angle}

given,

angle AOC + angle BOD = 242°

then,

angle AOC + angle AOC = 242°

=> 2 angle AOC = 242°

=> angle AOC = 242°/2

=> angle AOC = 121°

then,

angle AOC = angle BOD = 121°

now,

by fig,

angleAOC +angleBOD +angleAOD +angleBOC

=360°

=> 121° +121° + angleAOD +angleAOD

=360°

=> 242° + 2 angle AOD = 360°

=> 2 angle AOD = 360° - 242°

=> 2 angle AOD = 118°

=> angle AOD = 59°

then,

angle AOD = angle BOC = 59°

ANSWER:⤵️

angle AOC = 121°

angle BOD = 121°

angle AOD = 59°

angle BOC = 59°