Question

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

w =

x =

y =

Explanation:

Step1: Find angle \(x\)

Since \(\triangle BIG\sim\triangle MOP\), corresponding angles are equal. \(\angle B=\angle M\), \(\angle I=\angle O\), \(\angle G=\angle P\).
\(x = 29^{\circ}\) (corresponding angles of similar triangles)

Step2: Find angle \(w\)

Using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle).
\(w=180-(29 + 122)=29^{\circ}\)

Step3: Find side \(v\)

Set up a proportion for the sides. \(\frac{v}{18}=\frac{64}{96}\)
Cross - multiply: \(96v=64\times18\)
\(v=\frac{64\times18}{96}=12\)

Step4: Find side \(y\)

Set up a proportion for the sides. \(\frac{56}{y}=\frac{64}{96}\)
Cross - multiply: \(64y = 56\times96\)
\(y=\frac{56\times96}{64}=84\)

Answer:

\(v = 12\) m, \(w = 122^{\circ}\), \(x = 29^{\circ}\), \(y = 84\) m