Answer:
Options A , D , E
Explanation:
Triangle has angles 27° and 45°
The third angle = 180 - 27 - 45 = 108°
Therefore, the angles of ABC are 27° , 45° , 108°
=> ABC is Scalene triangle .
Option A :
Triangle DEF :
3x + 5x + 12x = 180°
20x = 180°
x = 9
Therefore , the angles of DEF = 27° , 45° , 108°
Satisfies
Option B:
Triangle GHI is Isosceles triangle with one angle 108°
But ABC is scalene , therefore not similar.
Does not satisfy.
Option C :
Triangle JKL with one of the angle = 72°
But none of the angles of ABC is equal to 72° .
Therefore, not similar.
Does not satisfy.
Option D :
Triangle MNO have angles 45° and 108°.
Sum of angles of triangles = 180°
So the third angle of MNO = 27°
Therefore , MNO is similar to ABC.
Satisfy.
Option E:
Angles of triangle PQR are 45° , x° , 4x°
Lets find all the angles .
45 + x + 4x = 180°
5x = 180 - 45
5x = 135
x = 27
Therefore, the angles of PQR = 45° , 27° , 108°
Hence similar to triangle ABC.
Satisfy
Option F :
Angles of triangle STU (5x + 3)°, (9x)° , (21x + 2)°
Sum of the angles => 5x + 3 + 9x + 21x + 3 = 180°
=> 35x = 180 - 5
=> 35x = 175
=> x = 5
Therefore, the angles are
5x + 3 = 5( 5) + 3 = 25 + 3 = 28°
9x = 9 ( 5 ) = 45°
21x + 2 = 21(5) + 2 = 105 + 2 = 107°
The angles are not congruent to the angles of Triangle ABC
does not satisfy.