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Question

# In the figure, AB = AC and AD || BC, find the respective measures of x, y and z.

A

x=70,y=70,z=55

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B

x=70,y=55,z=55

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C

x=55,y=55,z=55

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D

x=70,y=55,z=70

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Solution

## The correct option is B x=70∘,y=55∘,z=55∘ Given: AD || BC and AB = AC △ ABC is an isosceles triangle as its two sides are equal in length. ∴ y = z [Base angles of an isosceles triangle are equal] In △ ABC, x + y + z = 180∘ x + 2y = 180∘ ...(i) ∠EAD + ∠DAB + ∠BAC = 180∘ [Angles on a straight line] 55∘ + x + ∠DAB = 180∘ ∵ AD || BC, ∠DAB = y ∴ 55∘ + x + y = 180∘ x + y = 125 ...(ii) Solving (i) and (ii) x + 2y = 180∘ 2x + 2y = 250 - - - -------------------------- -x = -70 -------------------------- ⇒x=70∘ ⇒y=125−x=55∘ ⇒z=y=55∘ ∴ x, y and z are 70∘, 55∘ and 55∘ respectively.

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