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

Answer:

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.