Q. 265.0( 2 Votes )
State ‘True’ or ‘false’:
(i) A triangle can have two right angles.
(ii) A triangle cannot have two obtuse angles.
(iii) A triangle cannot have two acute angles.
(iv) A triangle can have each angle less than 60°.
(v) A triangle can have each angle equal to 60°.
(vi) There cannot be a triangle whose angles measure 10°, 80° and 100°.
Because, sum of angles of triangle equal to 180°.In a triangle maximum one right angle.
Because, obtuse angle measures in 90° to 180° and we know that the sum of angles of triangle is equal to 180°.
Because, in an obtuse triangle is one with one obtuse angle and two acute angles.
If each angles of triangle is less than 180° then sum of angles of triangle are not equal to 180°.
∠1 + ∠2 + ∠3 = 180°
If value of angles of triangle is same then the each value is equal to 60°.
∠1 + ∠2 + ∠3 = 180°
⇒ ∠1 + ∠1 + ∠1 = 180°[∠1 = ∠2 = ∠3]
⇒ 3 ∠1 = 180°
⇒ ∠1 = 60°
We know that sum of angles of triangle is equal to 180°.
Sum of angles,
= 10° + 80° + 100°
Therefore, angles measure in (10°, 80°, 100°) cannot be a triangle.
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