Question

Which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5

Answer 1

m<1 +m<2 = 180° is the answer

Answer 2

Third option is the right choice.

Step by step explanation:

We have been given an diagram and we are asked to choose the true statement about the diagram.

Let us see our all choices one by one.

1.
`m\angle5+m\angle6=m\angle1`

We can see that
`\angle5` and
`\angle6` are supplementary and there measure should be equal to 180 degrees.
`\angle1` is exterior angle of our triangle and its measure must be equal to sum of measures of
`\angle5` and
`\angle3`.

Therefore, 1st option is incorrect.

2.
`m\angle3+m\angle4+m\angle5=180^(o)`

We can see that
`\angle3` and
`\angle4` are supplementary and they must be equal to 180 degrees. Therefore, 2nd option is also incorrect.

3.
`m\angle1+m\angle2=180^(o)`

We can see from our diagram that
`\angle1` and
`\angle2` are supplementary. Therefore, 3rd option is the correct choice.

4.
`m\angle2+m\angle3=m\angle5`

We can see that
`\angle2`,
`\angle3` and
`\angle5` are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of
`\angle2` and
`\angle3` will be equal to measure of
`\angle6` instead of
`\angle5`.

Therefore, our 4th option is also incorrect.