Question

no irrelevant answers!​

Answer 1

x = 90°

y = 148°

z = 122°

Step-by-step explanation:

Because AC || DE,

so,

∠BEF = ∠ABE...[alternate interior angles are equal]

=> 122° = x + 32°

=> 122° - 32° = x

=> 90° = x

=> x = 90°

And,

∠y + 32° = 180...[sum of interior angles of same side is 180°]

=> y = 180° - 32°

=> y = 148°

Also,

z = 122°...[vertically opposite angles are equal]

used properties are in brackets

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Note :-

(see the attachment)

When two parallel lines cut by a transversal line,

• Alternate interior angles are equal [ ∠3 = ∠2, ∠5 = ∠8]
• Alternate exterior angles are equal [ ∠1 = ∠4, ∠6 = ∠7]
• Vertically opposite angles are equal [∠1 = ∠2, ∠3 = ∠4, ∠5 = ∠6, ∠7 = ∠8]
• Alternate angles of same side are equal [∠1 = ∠3, ∠2 = ∠4, ∠5 = ∠7, ∠6 = ∠8]
• Sum of interior angles of same side is 180° [∠2 + ∠5 = 180°, ∠3 + ∠8 = 180°]
• Sum of exterior angles of same side is 180° [∠1 + ∠6 = 180°, ∠4 + ∠7 = 180°]

Hope it helps.

#BeBraibly