Please who steps. on how to solve. ​

51°

Step-by-step explanation:

An inscribed angle is half of the arc it intercepts. This means that arc QR is twice m<QTR or 78°.

Since <QSR is a central angle, it equals the arc it intercepts. This means m<QSR equals arc QR which is 78°.

We can say that QS equals to RS because they are both radii, and radii of the same circle are equal. This means triangle QSR is isosceles.

Let <QRS equal x. Because of base angle theorem, <SQR would also be equal to x. Since the angles in a triangle add up to 180, we can write an equation to model the situation:

m<QRS + m<SQR + m<QSR = 180

We can substitute the values we have:

x + x + 78 = 180

2x = 102

x = 51

Since <QRS is equal to x, it is 51°

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

12cm

the answer is d