Based on the diagram shown, all of the following are true statements except

You are correct. The answer is choice C.

The other choices A, B, D have each side add up to 180 degrees either because the angles are a linear pair (adjacent and supplementary) or because the angles are same side interior angles. Same side interior angles are supplementary if a transversal line cuts through a pair of parallel lines as so happens in this diagram.

Step-by-step explanation:

We are given a triangle an a parallel line l to thr base of the triangle m.

l || m.

Let us check each statement one by one.

According to first statement

m<1 +m<2 = m<3+m<4

Angle m<1 and m<2 makes a linear pair and sum of linear pair angles is 180°.

Angle m< 3 and m < 4 also make a linear pair.

Therefore,  m<1 +m<2 = m<3+m<4 is correct.

Second statement

m<1 +m<5 = m<3+m<4

m<1 and m<5 are Consecutive Interior Angles and sum of Consecutive Interior Angles between two parallel lines is 180°.

Angle m< 3 and m < 4 also make a linear pair. Sum of those angles also 180°.

Therefore, m<1 +m<5 = m<3+m<4 statement is also correct.

Third Statement

It is not given that m<4 = m<6.

Therefore, we can't say m<1 +m<6 = m<4+m<6.

Fourth statement

m< 3 +m<4 = m<7+m<4

Angle m< 3 and m<4 makes a linear pair and sum of linear pair angles is 180°.

m<7 and m<4 are Consecutive Interior Angles and sum of Consecutive Interior Angles between two parallel lines is 180°.

Therefore, m< 3 +m<4 = m<7+m<4 is also true.

Finally we could say that third statement

m<1 +m<6 = m<4+m<6 is not true.

b

step-by-step explanation:

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -