Question

L || m

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


a. m∠1 + m∠2 = m∠3 + m∠4

b. m∠1 + m∠5 = m∠3 + m∠4

c. m∠1 + m∠6 = m∠4 + m∠6

d. m∠3 + m∠4 = m∠7 + m∠4

Answer 1

c. m∠1 + m∠6 = m∠4 + m∠6

Explanation:

Given: The lines l and m are parallel lines.

The parallel lines cut two transverse lines. Here we can use the properties of transverse and find the incorrect statements.

a. m∠1 + m∠2 = m∠3 + m∠4

Here m∠1 and m∠2 are supplementary angles add upto 180 degrees.

m∠3 and m∠4 are supplementary angles add upto 180 degrees.

Therefore, the statement is true.

b. m∠1 + m∠5 = m∠3 + m∠4

m∠1 + m∠5 = 180 same side of the adjacent angles.

m∠3 + m∠4 = 180, supplementary angles add upto 180 degrees.

Therefore, the statement is true.

Now let's check c.

m∠1 + m∠6 = m∠4 + m∠6

We can cancel out m∠6, we get

m∠1 = m∠4 which is not true

Now let's check d.

m∠3 + m∠4 = m∠7 + m∠4

We can cancel out m∠4, we get

m∠3 = m∠7, alternative interior angles are equal.

It is true.

Therefore, answer is c. m∠1 + m∠6 = m∠4 + m∠6