Question

△big is similar to △mop. find v, w, x, and y.
figure is not drawn to scale.
v = cm
w =
x =
y = cm

Explanation:

Step1: Use the property of similar triangles for angles

Since \(\triangle BIG\sim\triangle MOP\), corresponding angles are equal.
\(\angle B=\angle M = x^{\circ}\), \(\angle I=\angle O = 110^{\circ}\) (so \(w = 110\)), \(\angle G=\angle P=31^{\circ}\).
Using the angle - sum property of a triangle (\(\angle B+\angle I+\angle G = 180^{\circ}\)), \(x=180-(110 + 31)=39\).

Step2: Use the property of similar triangles for side - length ratios

The ratio of corresponding sides is \(\frac{36}{54}=\frac{2}{3}\).
For side \(v\): \(\frac{v}{27}=\frac{2}{3}\), cross - multiply gives \(3v=27\times2\), then \(v = 18\).
For side \(y\): \(\frac{22}{y}=\frac{2}{3}\), cross - multiply gives \(2y=22\times3\), then \(y = 33\).

Answer:

\(v = 18\) cm, \(w = 110\), \(x = 39\), \(y = 33\) cm