State true or false-If each angle of a triangle is than the of the other two angles of it then the triangle is acute-angled-TrueFalse

Question

Toppr Admin · Accepted Answer

Let the triangle be ABC-Sum of angles of the triangle-xA0-x2220-A-x2220-B-x2220-C-180-x2220-A-lt-x2220-B-x2220-C-x2220-A-lt-180-x2212-x2220-A-x2220-A-lt-90Similarly- -x2220-B-lt-90 and -x2220-C-lt-90Thus- ABC is an acute angled triangle-

State true or false:
If each angle of a triangle is less than the sum of the other two angles of it then the triangle is acute-angled.
True
False

Let the triangle be ABC,
Sum of angles of the triangle,
$∠ A + ∠ B + ∠ C = 180$
$∠ A < ∠ B + ∠ C$
$∠ A < 180 - ∠ A$
$∠ A < 90$
Similarly, $∠ B < 90$ and $∠ C < 90$
Thus, ABC is an acute angled triangle.

State true or false:If each angle of a triangle is less than the sum of the other two angles of it then the triangle is acute-angled.TrueFalse

Let the triangle be ABC,Sum of angles of the triangle, ∠A+∠B+∠C=180∠A<∠B+∠C∠A<180−∠A∠A<90Similarly, ∠B<90 and ∠C<90Thus, ABC is an acute angled triangle.

State true or false:
If each angle of a triangle is less than the sum of the other two angles of it then the triangle is acute-angled.
True
False

Let the triangle be ABC,
Sum of angles of the triangle,
$∠ A + ∠ B + ∠ C = 180$
$∠ A < ∠ B + ∠ C$
$∠ A < 180 - ∠ A$
$∠ A < 90$
Similarly, $∠ B < 90$ and $∠ C < 90$
Thus, ABC is an acute angled triangle.