Question

One of the acute angles of an obtuse angled triangle is one-third of the second one.
If the obtuse angle of the triangle is 120 degree,find the sizes of the two acute angles of the triangle.

Answer 1

The two acute angles of the triangle are 15° and 45° respectively.

Step-by-step explanation:

• Let,  first acute angle of triangle = α

• then second acute angle is = 3α       (Given)

• And obtuse angle = 120°         (Given)

As, we know that the sum of the three angles of a triangle is 180° .

• ∴   α + 3α + 120° = 180°

•     4α = 180° - 120° = 60°

•       α =60°/4 = 15° .

so, first acute angle of triangle (α) =15°

and second acute angle (3α) = 45°