Question

the given figure if angle AOR is equal to to 80 degree angle RQS is equal to 45 degree angle QRS equal to 35 degree prove that P parallel to M​

Answer 1

Answer:

In the given figure,

angle AOR = 80°

angle QSR = 35°

angle RQS = 45°

:. in triangle RQS,

angle QRS + angle RQS + angle QSR = 180° - (sum of measures of all angles in a triangle is 180°)

QRS + 45° + 35° = 180°

QRS + 80° = 180°

QRS = 100°

Also,

angle ORM =~ angle QRS - (vertically opposite angles)

since angle QRS = 100°

Therefore, angle ORM = 100°

angle AOR + angle ORM = 80° + 100°

therefore, angle AOR + angle ORM = 180°

THEREFORE, line P || line M - ( Interior angles test )

and OR is the transversal.

HENCE PROVED :)