15.(5 points) In the steel frame as shown in the figure, the steel frame is strengthened by welding 13 equal-length steel bars. If AP1= p1p2 = p2p3 = … = p13p14 = p14a, then

Source test paper:

20 13 analysis of mathematics test questions in Shaoxing city, Zhejiang province

Test center analysis:

triangle

Answer analysis:

Test center:

Properties of isosceles triangle.

Analysis:

Let ∠A=x, and calculate ∠AP7P8 and ∠AP8P7 according to the properties of equilateral angles and equilateral angles and the fact that an external angle of a triangle is equal to the sum of two non-adjacent internal angles, and then calculate according to the theorem of the sum of internal angles of a triangle.

Answer:

Solution: let ∠A=x,

∫AP 1 = p 1p 2 = P2P 3 =…= p 13p 14 = p 14A，

∴∠a=∠ap2p 1=∠ap 13p 14=x，

∴∠p2p 1p3=∠p 13p 14p 12=2x，

∴∠p2p3p4=∠p 13p 12p 10=3x，

…,

∠P7P6P8=∠P8P9P7=7x，

∴∠AP7P8=7x,∠AP8P7=7x，

In △AP7P8, ∠ a+∠ ap7p8+∠ ap8p7 = 180,

X+7x+7x = 180，

X = 12，

That is ∠ a = 12.

So the answer is: 12.

Comments:

This topic examines the properties of isosceles triangles with equal corners. An outer angle of a triangle is equal to the sum of two non-adjacent inner angles. It is difficult to explore the law.