In a general triangle ADE (as shown) lines EB and EC are drawn. Which of the following relations is true?

x + z = a + b

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y + z = a + b

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m + x = w + n

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x + y + n = a + b + m

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Solution

The correct option is D $x + y + n = a + b + m$
Exterior angles = Sum of internally opposite angles in a triangle
$∴$ z=w+n, n=b+a, m=y+x, c=w+m
x+y+n=x+y+b+a=m+b+a ( $∵$ m=y+x)
$∴$ x+y+n=a+b+m

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In a general triangle ADE (as shown) lines EB and EC are drawn. Which of the following relations is true?

The correct option is D x+y+n=a+b+mExterior angles = Sum of internally opposite angles in a triangle∴ z=w+n, n=b+a, m=y+x, c=w+mx+y+n=x+y+b+a=m+b+a (∵ m=y+x)∴ x+y+n=a+b+m

The correct option is D $x + y + n = a + b + m$
Exterior angles = Sum of internally opposite angles in a triangle
$∴$ z=w+n, n=b+a, m=y+x, c=w+m
x+y+n=x+y+b+a=m+b+a ( $∵$ m=y+x)
$∴$ x+y+n=a+b+m