Let's verify each case to determine the solution to the problem.
<u>Statements</u>
<u>case A)</u> m∠3 + m∠4 =
The statement is True
Because
Angle 3 and Angle 4 are supplementary angles
<u>case B)</u> m∠2 + m∠4 + m∠6 =
The statement is True
Because
The sum of the internal angles of a triangle is always equal to
<u>case C)</u> m∠2 + m∠4 = m∠5
The statement is True
Because
we know that
m∠2 + m∠4 + m∠6 = -----> equation A (see case B)
m∠5 + m∠6 = -------> by supplementary angles
m∠6 = -m∠5 -------> equation B
substitute equation B in equation A
m∠2 + m∠4 + -m∠5 =
m∠2 + m∠4 = m∠5 ---------> is ok
<u>case D)</u> m∠1 + m∠2=
The statement is False
Because
m∠1 + m∠2= -------> by supplementary angles
<u>case E)</u> m∠4 + m∠6=m∠2
The statement is False
Because
we know that
m∠2 + m∠4 + m∠6 =
m∠4 + m∠6 = -m∠2
m∠4 + m∠6=m∠2
-m∠2= m∠2
=2m∠2
m∠2=
the statement only will be true when the triangle be right triangle and
m∠2=
<u>case F)</u> m∠2 + m∠6 = m∠5
The statement is False
Because
we know that
m∠5 + m∠6 = -------> by supplementary angles
m∠5= -m∠6 -----> equation A
m∠2 + m∠6 = m∠5 --------> equation B (given equation)
substitute equation A in equation B
m∠2 + m∠6 = -m∠6
m∠2 + 2m∠6 =
the statement only will be true when the triangle be isosceles and
m∠4=m∠6
therefore
<u>the answer is</u>
m∠3 + m∠4 =
m∠2 + m∠4 + m∠6 =
m∠2 + m∠4 = m∠5