Question

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

Answer 1

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.

Answer 2

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

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

m<1 +m<6 = m<4+m<6

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.