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Byju's Answer
Standard IX
Mathematics
Proving Angle Sum Property
The sum of tw...
Question
The sum of two angles X and Y is 180° If X is an obtuse angle. Y is _____.
A
an acute angle
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B
an obtuse angle
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C
a right angle
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D
more than 180°
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Solution
The correct option is
A
an acute angle
As seen in this figure, the sum of X and Y is 180°,
∴ X + Y = 180°
⇒
Y = 180° - X
As X is obtuse angle, Y must be acute angle.
Example:
Let's take X = 100° (Obtuse angle)
100° + Y = 180°
⇒
Y = 80° (Acute angle)
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Which of the following statements are true (T) and which are false (F):
(i) Sum of the three angles of a triangle is 180°.
(ii) A triangle can have two right angles.
(iii) All the angles of a triangle can be less than 60°
(iv) All the angles of a triangle can be greater than 60°.
(v) All the angles of a triangle can be equal to 60°.
(vi) A triangle can have two obtuse angles.
(vii) A triangle can have at most one obtuse angles.
(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
(ix) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
(x) An exterior angle of a triangle is less than either of its interior opposite angles.
(xi) An exterior angle of a triangle is equal to the sum of the two interior opposite angles.