the diagram shows quadrilateral mnpq. what is the length of line segment mq? 8 units 10 units 11 units 15…

Explanation:

Step1: Identify right - angled triangle

Consider right - angled triangle MNQ. We know that NP = 3, PQ = 6, and MN = 10. Since NP is parallel to MQ, we can use the Pythagorean theorem in right - angled triangle MNQ.

Step2: Apply Pythagorean theorem

In right - angled triangle MNQ, if we assume the vertical side (height) is 6 and the hypotenuse MN = 10. Let the base MQ be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 10$ and $a = 6$. Then $x=\sqrt{10^{2}-6^{2}}$.

Step3: Calculate the value of MQ

First, calculate $10^{2}-6^{2}=100 - 36=64$. Then $\sqrt{64}=8$.

Answer:

8 units