If rt is a diameter of q, find m a.88°
b.89°
c.92°
d.101°

A.88°

Step-by-step explanation:

Given,

RT is the diameter of the circle with center Q.

We have to find the measure of ∠RQS.

Solution,

Since RT is the diameter. That is it makes a straight angle at the center Q.

And measure of straight angle is 180°.

So we can say that  ∠RQS and ∠SQT makes a straight angle.

Now substituting the given values, we get;

We get the value of 'x'.

By substituting the value of x, we can find the measure of ∠RQS.

Hence the measure of ∠RQS is 88°.

d

step-by-step explanation:

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.