By the traingle sum theorem, the sum of the angles in a triangle is 180°. Therefore, using the given and triangle sum theorem, m(∡P) + m(∡Q) + m(∡R) = 180°.
(5x)° + (5x)° + (8x)° = 180°. Simplifying the equation gets 18x=180°. Finally, using the division property of equality, x=10°.
Area of each side triangle is 1/2*8*15 = 60. There are 5 of them so the triangles have surface area 300. the pentagon's area 1/2*apothegm*sidelength*sides = 1/2*5.5*8*5 = 110. The total area is therefore 300+110 = 410
