Afootball player caught the ball and made a gain of 8 yards on the first play. on the next play the team lost 12 yards. how many yards do they need to gain on the next play to get back to their original position?

 The number of yards needed to gain on the next play to get back to their original position is 4.

Step-by-step explanation:  Given that a football player caught the ball and made a gain of 8 yards on the first play. On the next play the team lost 12 yards.

we are to find the number of yards needed to gain on the next play to get back to their original position.

Let, x be the number of yards that the team had originally.

So, on first day, the number of yards of the team is given by

On the next play, the team lost 12 yards, so the number of yards had on the second play will be

Let 'k' be the number of yards  needed to gain on the next play to get back to their original position.

So, we must have

Thus, the number of yards needed to gain on the next play to get back to their original position is 4.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.