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Question
In the given figure, what is z in terms of x and y?
Options
x + y + 180
x + y − 180
180° − (x + y)
x + y + 360°
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Solution
In the given ΔABC, we need to convert z in terms of x and y
Now, BC is a straight line, so using the property, “angles forming a linear pair are supplementary”
∠ABC + y = 180
∠ABC =180° - y°
Similarly,
∠ACB + x° = 180°
∠ACB = 180° - x
Also, using the property, “vertically opposite angles are equal”, we get,
z = ∠BAC
Further, using angle sum property of the triangle
∠BAC + ∠ABC + ∠ACB = 180°
z° + (180°- y°) + (180° - x°) = 180°
360° + z° - y° - x° = 180°
180° + z° = y° + x°
z° = y°+ x° -180°
Thus, z = y + x -180°
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