Question

in the fig AB parallel CD are cut by a transversal t at E and F respectively..if angle 1 =75° find the measure of the remaining angles​

Answer 1

$\huge{\underbrace{\sf{\red{Answer:}}}}$

$\large{\boxed{\sf{\purple{ \angle 1 = 75°, \angle 2 = 105°,\angle 3 = 75°}}}}$

$\large{\boxed{\sf{\purple{ \angle 4 = 105°, \angle 5 = 75°,\angle 6 = 105°}}}}$

$\large{\boxed{\sf{\purple{ \angle 7 = 75°, \angle 8 = 105°}}}}$

$\huge{\underbrace{\sf{\pink{Explanation:}}}}$

$\displaystyle{\sf{ \angle 1 + \angle 2 = 180°\:\:\:\:\:| \because\:Linear\:pair\:axiom}}$

$\implies{\sf{ 75° + \angle 2 = 180°}}$

$\implies{\sf{ \angle 2 = 180° - 75°}}$

$\implies{\sf{\angle 2 = 105°}}$

$\displaystyle{\sf{ \angle 2 = \angle 4 = 105°\:\:\:| \because Vertically\:Opposite\:Angle}}$

$\displaystyle{\sf{ \angle 1 = \angle 3 = 75°\:\:\:| \because Vertically\:Opposite\:Angle}}$

$\displaystyle{\sf{ \angle 2 = \angle 6 = 105°\:\:\:| \because Corresponding\:Angles}}$

$\displaystyle{\sf{ \angle 3 = \angle 7 = 75°\:\:\:| \because Corresponding\:Angles}}$

$\displaystyle{\sf{ \angle 4= \angle 8= 105°\:\:\:| \because Corresponding\:Angles}}$

$\displaystyle{\sf{ \angle 1 = \angle 5 = 75°\:\:\:| \because Corresponding\:Angles}}$

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