Final answer:
The length of ps is 2√5 units. The angle mqrs is 180 degrees.
Step-by-step explanation:
If the length of pq is 6 units, then the length of ps can be found using the Pythagorean theorem. Since ps is a diagonal of a right-angled triangle with pq as one of the sides, we can use the formula c² = a² + b² to find ps. In this case, pq is the hypotenuse and ps is one of the sides, so let's say ps = a and pq = c. Let the other side of the right-angled triangle be called pr = b. Using the formula, we have c² = a² + b². Substituting the given values, we get 6² = a² + b². Solving for a, we find that the length of ps is 2√5 units.
Regarding the second part of the question, the given angles madc and mbcdis can be used to find the angle mqrs. Since madc is 62 degrees and mbcdis is 118 degrees, the sum of these angles should be equal to mqrs. In other words, mqrs = madc + mbcdis = 62 + 118 = 180 degrees. Therefore, mqrs is 180 degrees.