Can someone help and give me a step by step explanation please?!

9514 1404 393

Step-by-step explanation:

The measure of an inscribed angle (QTR) is half the measure of the arc it intercepts. The measure of an arc is the same as the measure of the central angle it intercepts. So, we have ...

  ∠QSR = 2×∠QTR

  ∠QSR = 2×39°

  ∠QSR = 78°

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Sides SQ and SR are radii of circle S, so are the same length. That means triangle QRS is an isosceles triangle and the base angles SQR and SRQ are congruent. The sum of angles in a triangle is 180°, so we have ...

  ∠QSR + 2(∠SQR) = 180°

  78° + 2(∠SQR) = 180° . . . . fill in the value we know

  2(∠SQR) = 102° . . . . . . . . . subtract 78°

  ∠SQR = 51° . . . . . . . . . . . . .divide by 2

45

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .