Answer:
The sizes of the two acute angles of the triangle are 15° and 45°. Option (A) is true.
Explanation:
Given that one of the acute angles of an obtuse-angled triangle is one-third of the second one, and the obtuse angle of the triangle is 120°, we can solve for the sizes of the two acute angles.
Let's denote the two acute angles as A and B.
We know that one of the acute angles is one-third of the other, so we can express this as:
A = (1/3)B
We also know that the sum of the angles in a triangle is 180°, so we can express this as:
A + B + 120 = 180
Substituting the value of A from the first equation into the second equation gives us:
(1/3)B + B + 120 = 180
(4/3)B + 120 = 180
(4/3)B = 60
B = (3/4) * 60
B = 45
Substituting the value of B back into the first equation gives us:
A = (1/3) * 45
A = 15
So, the sizes of the two acute angles of the triangle are 15° and 45°.
Thus, Option (A) is true.