In the given figure, AB || CD || EF and AD || BE. Find x, y and z.

Question

KnowledgeBoat · Accepted Answer

Consider AB || CD and AD is a transversal: y° = 115° [Alternate angles] ∠BAD and ∠ABE are co-interior angles. Since, line GB intersects at point B, therefore ∠ABE = (x° + 30°) Co-interior angles are supplementary: ∴ ∠BAD + ∠ABE = 180° ⇒ 115° + x° + 30° = 180° [Substituting the value of ∠ABE] ⇒ x° + 145° = 180° ⇒ x° = 180° - 145° ⇒ x° = 35° Now, consider AB || EF and BE is a transversal: ∠BEF = ∠ABE [Alternate angles] ⇒ ∠BEF = x° + 30° [Substituting the value of ∠ABE] ⇒ ∠BEF = 35° + 30° [Substituting the value of x] ⇒ ∠BEF = 65° ∴ z° = 65° x° = 35°, y° = 115° and z° = 65°

Mathematics

In the given figure, AB || CD || EF and AD || BE. Find x, y and z.

Lines & Angles

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