Question

Getting k equals B and J C find the value of a s

Answer 1

Given that

`\begin{gathered} \angle K\cong\angle D \\ \angle J\cong\angle C \end{gathered}`

By the AA-similarity postulate, those triangles are similar, therefore

`\angle L\cong\angle B`

Since those angles are congruent, their measures are equal.

`m\angle L=m\angle B`

Using the property that states the sum of the inside angles of a triangle is equal to 180º, since we have the measures of ∠C and ∠D, we can easily calculate m∠B.

We have the following relation

`\begin{gathered} m\angle C+m\angle D+m\angle B=180^o \\ \Rightarrow35^o+90^o+m\angle B=180^o \\ \Rightarrow m\angle B=180^o-35^o-90^o=55^o \end{gathered}`

Now that we have m∠B and m∠L(in terms of s), we can rewrite our previous equation as

`m\angle L=m\angle B\Rightarrow3s-20=55`

Solving it for s, we have

`\begin{gathered} 3s-20=55 \\ 3s=55+20 \\ 3s=75 \\ s=(75)/(3) \\ s=25 \end{gathered}`

And this is our result.

s = 25.