Question

which statements are always true regarding the diagram? Check all that apply.

Answer 1

Answer:

first three

Step-by-step explanation:

quizlet

Answer 2

The true statements regarding the diagram are:

$m\angle 3+m\angle 4=180^{\circ}\\\\m\angle 2+m\angle 4+m\angle 6=180^{\circ}\\\\m\angle 2+m\angle 4=m\angle 5$

What is interior angle?

"It is an angle inside a polygon."

What is exterior angle?

"It is the angle between a side of a polygon and an extended adjacent side."

For given question,

We know, the sum of an adjacent interior angle and exterior angle is always equal to 180°.

⇒ $m\angle 1+m\angle 2=180^{\circ}$

⇒ $m\angle 3+m\angle 4=180^{\circ}$

⇒ $m\angle 5+m\angle 6=180^{\circ}$                    ...................(i)

We know, the sum of all angles of triangle is 180°

⇒ $m\angle 2+m\angle 4+m\angle 6=180^{\circ}$            ..............(ii)

From (i),

$m\angle 6=180^{\circ}-m\angle 5$

So, equation (ii) would be,

⇒ $m\angle 2+m\angle 4+ 180^{\circ}-m\angle 6=180^{\circ}$

⇒ $m\angle 2+m\angle 4=m\angle 5$

Therefore, the true statements regarding the diagram are:

$m\angle 3+m\angle 4=180^{\circ}\\\\m\angle 2+m\angle 4+m\angle 6=180^{\circ}\\\\m\angle 2+m\angle 4=m\angle 5$

Learn more about interior and exterior angle here:

https://brainly.com/question/10638383

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