The first quartile of the given data is 35. find the value of x.
X 0-20/20-40/40-60/60-80/80-100
F 2 x 8 5 1

The given value of the first quartile is related to the value cumulative

frequency up to the class of the first quartile.

Reasons:

The first quartile is one of the five number summary.

The number of terms, N = 2 + x + 8 + 5 + 1 =16 + x

We have;

Where;

The first quartile, Q₁ = 35

L = 20 in the first quartile class

PCF = The cumulative frequency of the first quartile class = 2 + x

f = The frequency of the quartile class = x

C = The class size = 10

Therefore;

Which gives;

Therefore;

70·x = 25·x + 45

45·x = 45

x = 45 ÷ 45 = 1

Learn more about the five number summary here:

link

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.