Question

In the figure, if a ray MN stands on the line AB such that ∠ANM = ∠MNB, then show that ∠AMN = 90°

Answer 1

Here,

Given that,

angle ANM=angle MNB=x(let)

Also,

angle ANM+ angle MNB=180°[Being linear pair]

or, x+x=180°

or,2x=180°

or, x=90°

So,angle ANM=angle MNB=90°

Hence, proved.

Answer 2

/_ ANM+/_ MNB =180 (SUM OF LINEAR ANGLE PAIR )

SO

/_ 90+ /_ MNB= 180

/_MNB=180-90= 90