Question

In each of the following figures, find x and y when AB।।CD ​

Answer 1

Answer:

(i)

AB || CD

=> X = 64⁰

angle sum property of triangle is 180⁰

A + B + BCA = 180⁰

72⁰ + 64⁰ + BCA = 180⁰

136⁰+ BCA = 180⁰

BCA = 180⁰-136⁰

BCA = 44⁰

BCA + X + y = 180⁰(linear pair)

44⁰ + 64⁰ + y = 180⁰

108⁰ + y = 180⁰

y = 180⁰-108⁰

y = 72⁰

ii)

AB || CD

=> y = 63⁰

angle sum property of triangle is 180⁰

ACB + 57⁰ + 63⁰ = 180⁰

ACB + 120⁰ = 180⁰

ACB = 180⁰-120⁰

ACB = 60⁰

ACB + y + x = 180⁰(linear pair)

60⁰ + 64⁰ + x = 180⁰

124⁰+ x = 180⁰

x = 180⁰-124⁰

x = 56⁰

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