Question

6.2 assignment
possible points: 0.67
find the value of x.
(figure with angles 90°, 60°, 4x°, x°, 2x°)
x =

Explanation:

Step1: Sum of angles in a pentagon? No, it's a polygon with angles around a point? Wait, actually, the sum of the exterior angles of any polygon is 360 degrees? Wait, no, here we have a figure with angles: 90°, 60°, 4x°, x° (wait, no, the 2x° and x°: actually, the 2x° and x° are supplementary? Wait, no, let's look at the angles. The figure has angles: 90°, 60°, 4x°, and then the other two angles: 2x° and its adjacent angle x°? Wait, no, actually, the sum of the angles around a point? Wait, no, it's a polygon where the sum of the interior angles? Wait, no, let's count the angles. The angles given are 90°, 60°, 4x°, and then the two angles: 2x° and x°? Wait, no, the 2x° and x°: actually, 2x° and x° are adjacent, so 2x + x = 3x? Wait, no, maybe the sum of all angles is 360°? Wait, no, let's think again. The figure has angles: 90°, 60°, 4x°, and then the other two angles: 2x° and (180 - x)°? No, that's not right. Wait, maybe it's a pentagon? No, the sum of the interior angles of a pentagon is (5-2)180 = 540°, but here we have angles: 90°, 60°, 4x°, 2x°, and x°? Wait, 90 + 60 + 4x + 2x + x = 540? Wait, 90+60=150, 4x+2x+x=7x, so 150 + 7x = 540? Then 7x=390? No, that can't be. Wait, maybe it's a quadrilateral? No, the figure has five angles? Wait, no, the diagram: let's see, the angles are 90°, 60°, 4x°, and then two angles: 2x° and x°, but maybe the 2x° and x° are actually supplementary to each other? Wait, no, the 2x° and x°: if they are on a straight line, 2x + x = 180? No, that would be 3x=180, x=60, but then 4x=240, 90+60+240=390, which is more than 360. Wait, maybe the sum of the exterior angles? No, exterior angles sum to 360. Wait, let's re-express the angles. The angles given are 90°, 60°, 4x°, and then the other two angles: 2x° and x°, but actually, the 2x° and x°: maybe the 2x° is an interior angle, and x° is an exterior angle? No, this is confusing. Wait, let's look at the correct approach. The sum of the angles in the figure (a pentagon? No, maybe a quadrilateral with a triangle? Wait, no, the correct way: the sum of the angles around a point is 360°, but here we have angles: 90°, 60°, 4x°, and then the two angles: 2x° and x°, but actually, 2x° and x°: wait, 2x + x = 3x, and then 90 + 60 + 4x + 3x = 360? Wait, 90+60=150, 4x+3x=7x, so 150 + 7x = 360? Then 7x=210, so x=30. Let's check: 90+60+430+2*30+30=90+60+120+60+30=360. Yes! So that works. So the sum of all angles is 360°, so:

Step1: Sum of all angles = 360°

90 + 60 + 4x + 2x + x = 360

Step2: Simplify the left side

90 + 60 = 150; 4x + 2x + x = 7x
So 150 + 7x = 360

Step3: Solve for x

7x = 360 - 150
7x = 210
x = 210 / 7
x = 30

Answer:

30