Question

Determine the following:
(Iin the figure, x: y = 3:5 and ZACD = 160°. Find the value of x, y andz​

Answer 1

Answer:

Given: AB∥CD

Given: AB∥CD∠BAD=∠CDA=36

Given: AB∥CD∠BAD=∠CDA=36 ∘

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AE

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE∠ACE+∠AEC+∠CAE=180 (Angle sum property)

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE∠ACE+∠AEC+∠CAE=180 (Angle sum property)z+68+68=180

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE∠ACE+∠AEC+∠CAE=180 (Angle sum property)z+68+68=180z=180−136

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE∠ACE+∠AEC+∠CAE=180 (Angle sum property)z+68+68=180z=180−136z=44

Given: AB∥CD∠BAD=∠CDA=36 ∘ (Alternate angles)∠AEC=∠ECD+∠EDC (Exterior angle property)∠AEC=32+36∠AEC=68 ∘ Since, AC=AEy=∠AEC=68 ∘ (Isosceles triangle property)In △ACE∠ACE+∠AEC+∠CAE=180 (Angle sum property)z+68+68=180z=180−136z=44 ∘