Question

δabc is similar to δedc. find v, w, x, and y.
figure is not drawn to scale.
v =
w =
x = in.
y = in.

Explanation:

Step1: Find \(v\)

Vertical angles are equal. So \(v = 29^{\circ}\)

Step2: Find \(w\)

Sum of angles in a triangle is \(180^{\circ}\).
For \(\triangle ABC\) and \(\triangle EDC\), since they are similar.
In \(\triangle ABC\), angles are \(100^{\circ},29^{\circ},B\). In \(\triangle EDC\), angles are \(w^{\circ},29^{\circ},E\).
Using angle - sum property: \(100 + 29+ B=180\) and \(w + 29+E = 180\). Also, \(B = E\) (similar triangles).
\(w=180-(29 + 51)=51^{\circ}\) (because \(B=180-(100 + 29)=51^{\circ}\))

Step3: Use similarity ratio for sides

Since \(\triangle ABC\sim\triangle EDC\), the ratio of corresponding sides is equal.
\(\frac{63}{36}=\frac{84}{y}=\frac{x}{12}\)
First, find \(y\):
\(\frac{63}{36}=\frac{84}{y}\)
Cross - multiply: \(63y=36\times84\)
\(y=\frac{36\times84}{63}=48\)

Step4: Find \(x\)

Using \(\frac{63}{36}=\frac{x}{12}\)
Cross - multiply: \(36x=63\times12\)
\(x=\frac{63\times12}{36}=21\)

Answer:

\(v = 29\), \(w = 51\), \(x = 21\), \(y = 48\)