Which statements are always true regarding the diagram? check all that apply.
m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
m∠4 + m∠6 = m∠2
m∠2 + m∠6 = m∠5

Let's verify each case to determine the solution to the problem.

Statements

case A) m∠3 + m∠4 =

The statement is True

Because

Angle 3 and Angle 4 are supplementary angles

case B) m∠2 + m∠4 + m∠6 =

The statement is True

Because

The sum of the internal angles of a triangle is always equal to  

case C) 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

case D) m∠1 + m∠2=

The statement is False

Because

m∠1 + m∠2= -------> by supplementary angles

case E) 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=

case F) 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

the answer is

m∠3 + m∠4 =

m∠2 + m∠4 + m∠6 =

m∠2 + m∠4 = m∠5

45

step-by-step explanation: