Answer:
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
