Question

in the given figure a b parallel to CD BC parallel D E then find the values of X and Y​

Answer 1

Answer:

X = 34

Y = 54

Step-by-step explanation:

∠BAC = ∠DCE   [ab and dc are parallel they will subtend same angle at AE]

∠BAC = 24°

∠BCA  + ∠BCD + ∠DCE = 180° [STRAIGHT LINE]

∠BCA = 180° - (∠BCD + ∠DCE)

∠BCA = 180° - (105° + 24°)

∠BCA = 51°

∠ABC + ∠BCA + ∠BAC = 180° [ TRIANGLE]

∠ABC = 180 - (∠BCA + ∠BAC)

∠ABC = 180° - (54° + 24°)

∠ABC = 102°

∠ABC = 3X

$x = \frac{∠ABC}{3}\\ x = \frac{102°}{3} \\x = 34°$

∠DEC = ∠BCA [BC AND DE ARE PARALLEL SO ANGLE SUBTENDED BY THEM WITH ACE WILL BE EQUAL]

y = ∠DEC = 54°