Is this triangle question missing information?

Question

In the $\Delta KLP$, find $a+b$:

My question is that: isn't some information missing from the question? Because all I can see is is that $ \usepackage{ gensymb }

\angle SKP = \angle LTS = p\degree $.

Am I missing some well known formula ??

Please help me with some hints/guides.

Answer 1

Since the triangles $STL$ and $PKL$ are similar, we know the ratios of their sides are the same:

$$\frac{a}{9}=\frac{10}{b+8}=\frac{8}{12}$$

Hence $a=(9)\frac{2}{3}=6$ and $2b+16=30$, hence $b=7$. Finally we have $a+b=13$.

Answer 2

Hint: You are missing the fact that the big triangle and the little triangle are similar.

Answer 3

Hint Please note that $\angle SLT$ is a common angle for $\triangle SLT$ and $\triangle KLP$, and yes, as you noted, the triangles have another pair of equal angles. Now, what do we say about two triangles who have two equal pairs of angles?