Which statements are always true regarding the diagram?
select three option. (picture included)
m< 5+m< 3=m< 4
m< 3+m< 4+m< 5=180
m< 5+m< 6=180
m< 2+m< 3=m< 6
m< 2+m< 3+m< 5=180

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 > equation A

we know that

m∠3+m∠4=180° > by supplementary angles

m∠4=180°-m∠3 > equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° > equation A

we know that

m∠3+m∠4=180° > by supplementary angles

m∠4=180°-m∠3 > equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 > equation A

we know that

m∠5+m∠6=180° > by supplementary angles

m∠6=180°-m∠5 > equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

y > 1/3x

y < = -x + 4

hope this : )