When a dilation is performed we get two similar shapes, the original one (BCD in this case) and a smaller one (B'C'D'), since the figures are similar the measures of corresponding angles are the same and then m
The three angles of a triangle add up to 180°, then we can formulate the following expression:
m
By replacing 51° for m
m
Solving for m
mmmm
Since mm
The dilation was performed with a scaling factor of 1/2, this means that the lengths of the sides of the shape figure are 1/2 times the size of the sides of the original shape. then we can formulate the following expression for CQ and C'Q:
C'Q = CQ×1/2
By multiplying ob both sides of this expression by 2 we get:
2C'Q = CQ
CQ = 2(3)
CQ = 6
Then CQ = 6
Similarly, for B'D' and BD:
B'D' = BD×1/2
B'D' = 22×1/2
B'D' = 22/2
B'D' = 11
Then B'D' = 11