Question

in the given figure find the values of x and y if AB||CD​

Answer 1

Answer:

x = 22°

y = 58°

for explanation refer to attachment

verification :

in triangle PQR sum of all angles = 180°

angle PQR + QRP + RPQ = 180°

58° + 100° + 22° = 180°

hence proved ...

Answer 2

SOLUTION :-

We know that interior angles are equal to each other,

→ 58° = 20° + ∠y

→ ∠y = 58° - 20°

→ ∠y = 38°

Now,

→ ∠a + 22° = 180°- (20° + ∠y)

→ ∠a + 22° = 180° - 58°

→ ∠a = 122° - 22°

→ ∠a = 100°

Now value of ∠x,

→ ∠x + ∠y + ∠a = 180°

→ ∠x + 38° + 100° = 180°

→ ∠x = 180° - 138°

→ ∠x = 42°

Hence the value of x and y is 42° and 38° respectively.