Question

Give reasons for your answer
can a triangle have
two acute angles
two obtuse angles
two right angles
all angles more than 60 °
all angles less than 60 °
all angles of measure 60 °
​

Answer 1

Answer:

No, a triangle cannot have all angles less than 60°, because if all angles will be less than 60°, then their sum will not be equal to 180°. Hence, it will not be a triangle.

Step-by-step explanation:

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Answer 2

Answer:

yes

no

no

no

yes

yes

step by step instructions:

• sum of all angles of a triangle = 180°
• Two acute angles :
• acute angle means less than 90°
• if we take 1st angle to be : 45° { just assumption}
• 2nd angle : 60°
• if we know 1st and 2nd angles we can easily find 3rd angle by the formula sum of all angles is 180° so , 3rd angle : 75°
• a triangle is possible as two of them are acute and follows the rule of sum of angles
• Two obtuse angles :
• obtuse means more than 90°
• if we take 1st angle : 95°
• 2nd angle : 100°
• it is not possible as the sum of two angles is 195° and it does not obey the rule of sum of all angles
• Two right angles
• so both angles are 90°
• the sum of two angles is 180° and other angle cannot be zero*
• all angles more than 60°
• so 1st angle = 65°
• 2nd angle = 70°
• 3rd angle = 75°
• sum of all angles is more than 180°
• so this triangle is not possible
• all angles less than 60°
• so 1st angle = 55°
• 2nd angle = 50°
• 3rd angle = 45°
• the sum of all angles is less than 180°
• so this triangle is also not possible
• all angles are 60°
• which means 1st 2nd and 3rd angles are 60°
• summ of all angles 60+60+60 = 180°
• so this triangle is possible

• all angles are taken by assuming only if you have any doubt you can take other angles also