Answer:
v = 40 cm
w = 126
x = 30
y = 63 cm
Explanation:
So are given that ΔBIG is similar to ΔMOP. This means that their respective angles are the same measurements, but different side lengths. By definition of similar triangles, their respective side lengths are equal in proportion.
∠I corresponds to ∠O, so their measurements are equal. w = 126°.
∠B corresponds to ∠M, so their measurements are also equal. We don't know the angle measurement for x, but we have all the angles for two similar triangles, so we can find the measure of the third angle. The total angle measure for any triangle is 180°.
x = 180 - 24 - 126
x = 30°
Now that we have all the angle measurements, we can proportions to calculate the lengths of the unknown sides. The proportion of ΔBIG to ΔMOP can be calculated using the corresponding side length for each triangle.
Segment BG corresponds to segment MP. The proportion of BG to MP is:
48/72. Proportions are fractions, so this ratio can be simplified to 2/3 (divide by 24 on top and bottom).
Now we know that the ratio of ΔBIG to ΔMOP is 2/3.
Segment BI (aka v) = (2/3) * 60 cm
v = 40 cm
Segment PO (aka y) * (2/3) = 42 cm
y = 42 * 1.5
y = 63 cm