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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: AB || 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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