Basic Geometry

[bronx.system]

hey all very simple question but cant solve the problem.

i have to find value of the pro-numerals:

i understand that a and b are supplementary but thats where i get stuck.

for some reason i get right answer when i
a + 135 + 70 = 360
a = 155

but not sure why that works S:

therefore 155 + b = 180 (this part supplementary i understand)
b = 25

so i can get the answer but dont understand why the first step worked. is there a better way?

 

[serds]

This is a pentagon. The sum of the internal angles is 540°.
That's why 540°-2*90°-135°-70°=155°


I would have tried it with the sum of the angles in a triangle.
The angles c+135° and d+70°+e° must be together 180°.
c=180°-135°=45°; d=180°-90°-45°=45°; e=180°-70°-45°=65°
-> b= 180°-90°-65°=25° -> a=180°-25°=155°

 

[bronx.system]

oohhh yes thats right.

quadrilaterals 360
and hexagon would be 4x180 = 720

i remember now
thank you very much.

EDIT: thanks for the second part too that made it clearer

 

[HallsofIvy]

I would have done this a slightly different way. We are given the angle 135 degrees at the top. Its supplementary angle is 180- 135= 45 degrees. That angle is then part of a right triangle. The two acute angles must add to 90 degrees so the other angle is also 90- 45= 45 degrees. That, together with the given 70 degree angle adds to 70+ 45= 115 degrees. And since the three angles one the right must add to 180 degrees, the remaining angle there is 180- 115= 65 degrees. And it and angle "b" are acute angles in a right triangle so must add to 90 degrees. b= 90- 65 and a, of course, is 180- b.