Which of the following statements must be true about this diagram? check all that apply.

The correct options are:

Option: A

Option: B

and Option: E

Step-by-step explanation:

With the help of the figure attached to the answer we could clearly observe that ∠4 is an obtuse angle whereas ∠1,∠2,∠3 are acute angle i.e. there measure are less than 90°.

Also, we know that:

m∠3+m∠4=180°

i.e.

m∠3=180°-m∠4(1)

( Since the angles formed by a straight line are of measure 180 degree)

Also we know that the sum of all the angles of a triangle is 180 degree.

Hence, we have:

m∠1+m∠2+m∠3=180°

on using equation (1) we have:

m∠1+m∠2+180°-m∠4=180°

m∠1+m∠2-m∠4=180°-180°

m∠1+m∠2-m∠4=0

m∠1+m∠2=m∠4

( Also as ∠4 is formed by the addition of ∠1 and ∠2 hence it's measure has to be greater than both of them)

Hence, the correct options are:

m∠4 is greater than m∠2.

m∠4 is greater than m∠1.

m∠1+m∠2=m∠4

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