Question

The two triangles DAS and UIP are congruent. Find the value of $\angle ADS$ (in degrees).

Answer 1

Since the two triangles are congruent, they have the same measure of side lengths as well as interior angles.

If $\angle UPI$ is ${38}^o$, by the property of congruency, $\angle DSA$ is also ${38}^o$.

It is also given that triangle, $△DAS$ is an isosceles triangle as the sides $DA$ and $DS$ are equal.
$\therefore \angle DAS=\angle DSA$
$\Rightarrow \angle DAS={38}^o$

Also, in any triangle the sum of all $3$ interior angles is equal to $180$ degree.

$\therefore {38}^o+{38}^o+\angle ADS={180}^o$
So, $\angle ADS={104}^o$.