Answer:
50.74 degrees
Step-by-step explanation:
To find the value of the unknown angle, we have to find the value of the angle RQP.
Since we have the lengths of the 3 sides, it's easy with the Cosines Law, that says:
[tex]cos(A) = \frac{b^{2} + c^{2} - a^{2}}{2 * b * c}[/tex]
So, let's say a = 151, b = 77 and c = 90
If we isolate A, which is our Q in the figure, we get:
[tex]A = cos^{-1} (\frac{b^{2} + c^{2} - a^{2} }{2 * b * c} ) = cos^{-1} (\frac{77^{2} + 90^{2} - 151^{2} }{2 * 77 * 90} ) = 129.26[/tex]
We now know that angle RQP is 129.26 degrees.
Since the line PQ is extended... we know this forms a 180 degree flat angle. If we then subtract the 129.26 degrees from the 180 angle, we get 50.74 degrees.
