if δpqr is dilated by a scale factor of 2 with a dilation center at vertex q, which statement is true?
a) the angle measurements decrease by a factor of
1
2
.
b) the angle measurements decrease by a factor of 2.
c) the angle measurements increase by a factor of 2.
d) the angle measurements are unchanged.

Option D) The angle measurements are unchanged.

Step-by-step explanation:

we know that

A dilation is a non-rigid transformation that produces an image that is the same shape as the original, but is a different size, so produces similar figures.

Remember that, if two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent.

therefore

The angle measurements are unchanged

i got 10.28 but that rounds up to 10.3

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.