342
Question
If the sum of all the angles of a triangle is 180°, then at least ____ angle/angles of the triangle will be acute.
If the sum of all the angles of a triangle is 180°, then at least ____ angle/angles of the triangle will be acute.
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Solution
The correct option is A 2
If one of the angles of the triangle is 90°, then the sum of the other two angles will be 180° − 90° = 90°.
It means the other two angles will be acute angles.
If one of the angles of the triangle is obtuse, then the sum of the other two angles will be less than 90°.
It means the other two angles will be acute angles.
In other cases, all the three angles of the triangle will be acute angles.
So, at least 2 angles of the triangle must be acute angles.
Hence, option c is the correct answer.
If one of the angles of the triangle is 90°, then the sum of the other two angles will be 180° − 90° = 90°.
It means the other two angles will be acute angles.
If one of the angles of the triangle is obtuse, then the sum of the other two angles will be less than 90°.
It means the other two angles will be acute angles.
In other cases, all the three angles of the triangle will be acute angles.
So, at least 2 angles of the triangle must be acute angles.
Hence, option c is the correct answer.
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