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

M∠3 + m∠4 = 180°  ( RIGHT)
m∠2 + m∠4 + m∠6 = 180° ( RIGHT)
m∠2 + m∠4 = m∠5 ( RIGHT)
m∠1 + m∠2 = 90° (WRONG)
m∠4 + m∠6 = m∠2  (WRONG)
m∠2 + m∠6 = m∠5  (WRONG)

M∠3 + m∠4 = 180°  ( RIGHT)
m∠2 + m∠4 + m∠6 = 180° ( RIGHT)
m∠2 + m∠4 = m∠5 ( RIGHT)
m∠1 + m∠2 = 90° (WRONG)
m∠4 + m∠6 = m∠2  (WRONG)
m∠2 + m∠6 = m∠5  (WRONG)

m∠3 + m∠4 = 180°
As these 2 angles make up a straight line, the sum of the magnitude of angles is 180° so this is true 

m∠2 + m∠4 + m∠6 = 180°
these 3 angles are the interior angles of a triangle. the sum of all the interior angles of a triangle sum up to 180° so this is true.

m∠2 + m∠4 = m∠5
for this statement, use the previously stated concepts 
m∠2 + m∠4 + m∠6 = 180°
m∠5 + m∠6 = 180°
since both equations are equal lets put them into one equation
m∠2 + m∠4 + m∠6 =m∠5 + m∠6
since m∠6 is common for both sides lets cancel it out which leaves us with 
m∠2 + m∠4 = m∠5
therefore this statement is true 

m∠1 + m∠2 = 90°
sum of the angles making up a straight line is 180 °, therefore this is incorrect

m∠4 + m∠6 = m∠2
lets use the following equation
m∠2 + m∠4 + m∠6 = 180° 
if m∠6 + m∠4 = m∠2
then using this we substitute in the previous equation
m∠2 + ∠m∠2 = 180°
m∠2 = 90°
so this angle should be a right angle, but in the diagram its not a right angle therefore this is incorrect 

m∠2 + m∠6 = m∠5
since 
m∠5 + m∠6 = 180°
m∠2 + m∠4 + m∠6 = 180° 
then putting both the equations in one as they are both equal
m∠2 + m∠4 + m∠6 = m∠5 + m∠6
this shows that 
m∠2 + m∠4 = m∠5 
then m∠4 should be equal to m∠6
but judging from the sides opposite to the angles m∠4 and m∠6 the sides aren't equal so these angles too cannot be equal so this statement is wrong.

m∠3 + m∠4 = 180°
As these 2 angles make up a straight line, the sum of the magnitude of angles is 180° so this is true 

m∠2 + m∠4 + m∠6 = 180°
these 3 angles are the interior angles of a triangle. the sum of all the interior angles of a triangle sum up to 180° so this is true.

m∠2 + m∠4 = m∠5
for this statement, use the previously stated concepts 
m∠2 + m∠4 + m∠6 = 180°
m∠5 + m∠6 = 180°
since both equations are equal lets put them into one equation
m∠2 + m∠4 + m∠6 =m∠5 + m∠6
since m∠6 is common for both sides lets cancel it out which leaves us with 
m∠2 + m∠4 = m∠5
therefore this statement is true 

m∠1 + m∠2 = 90°
sum of the angles making up a straight line is 180 °, therefore this is incorrect

m∠4 + m∠6 = m∠2
lets use the following equation
m∠2 + m∠4 + m∠6 = 180° 
if m∠6 + m∠4 = m∠2
then using this we substitute in the previous equation
m∠2 + ∠m∠2 = 180°
m∠2 = 90°
so this angle should be a right angle, but in the diagram its not a right angle therefore this is incorrect 

m∠2 + m∠6 = m∠5
since 
m∠5 + m∠6 = 180°
m∠2 + m∠4 + m∠6 = 180° 
then putting both the equations in one as they are both equal
m∠2 + m∠4 + m∠6 = m∠5 + m∠6
this shows that 
m∠2 + m∠4 = m∠5 
then m∠4 should be equal to m∠6
but judging from the sides opposite to the angles m∠4 and m∠6 the sides aren't equal so these angles too cannot be equal so this statement is wrong.

m∠5 + m∠3 = m∠1  is true.
Explanation:
m∠1 + m∠2 = 180                   (sum of angles on a straight line)   (1)
or m∠2 = 180 - m∠1                                                                         (2)
m∠2 + m∠5 + m∠3 = 180       (sum of angles in a triangle)           (3)
Substitute (2) into (3) to obtain
180 - m∠1 + m∠5 + m∠3 = 180 
m∠5 + m∠3 = m∠1 

m∠5 + m∠6 = 180 is true
Explanation:
Sum of angles on a straight line is 180 deg.

m∠2 +m∠3 = m∠6  is true
Explanation:
The proof is similar as for the first statement.

m∠2 +m∠3 +m∠5 = 180  is true
Explanation:
Sum of angles in a triangle is 180 deg.

m∠5 + m∠3 = m∠1  is true.
Explanation:
m∠1 + m∠2 = 180                   (sum of angles on a straight line)   (1)
or m∠2 = 180 - m∠1                                                                         (2)
m∠2 + m∠5 + m∠3 = 180       (sum of angles in a triangle)           (3)
Substitute (2) into (3) to obtain
180 - m∠1 + m∠5 + m∠3 = 180 
m∠5 + m∠3 = m∠1 

m∠5 + m∠6 = 180 is true
Explanation:
Sum of angles on a straight line is 180 deg.

m∠2 +m∠3 = m∠6  is true
Explanation:
The proof is similar as for the first statement.

m∠2 +m∠3 +m∠5 = 180  is true
Explanation:
Sum of angles in a triangle is 180 deg.

The statements that are always true regarding the diagrams are mentioned below:

1) m∠5 + m∠3 = m∠1

2) m∠5 + m∠6 = 180°

3) m∠2 + m∠3 = m∠6

4) m∠2 + m∠3 + m∠5= 180° 

thus, only one statement i..e m∠3 + m∠4 + m∠5 = 180° does not apply correctly. Rest all statements are valid.

The statements that are always true regarding the diagrams are mentioned below:

1) m∠5 + m∠3 = m∠1

2) m∠5 + m∠6 = 180°

3) m∠2 + m∠3 = m∠6

4) m∠2 + m∠3 + m∠5= 180° 

thus, only one statement i..e m∠3 + m∠4 + m∠5 = 180° does not apply correctly. Rest all statements are valid.