The points A,B,C and D are consecutive vertices of a regular polygons with 20 sides.Calculate angles
(a) ABC
(b) ACD
(c) ABD
Ah. I see what I did wrong.
Since ∆ABC is an isosceles ∆ with vertex angle of 162°, its two base angles (∡BAC and ∡BCA) are each 9°. So, ∡ACD = ∡ABD = 162-9 = 153°.
If you draw the diagram of vertices A,B,C,D this is clear.
every interior angle has measure 18*180/20 = 162°
So, any angle formed by three vertices will be a multiple of that.
but the answer of (a).162 (b).153 (c).153
gee. so which choice is a multiple of 162???!!!
come on ...
I understand the 162,but how comes 153
I got It. Thanks.
(a) 162 (b) 153 (c) 153
(i)162 (ii) 153 (iii) 153
To calculate the angles ABC, ACD, and ABD in a regular polygon with 20 sides, you need to understand the properties of regular polygons.
A regular polygon is a polygon in which all sides are of equal length and all angles are of equal size.
The formula to calculate the interior angle of a regular polygon is:
Interior angle = (n-2) * 180° / n
Where:
- n is the number of sides of the polygon.
Now, let's calculate the angles:
(a) Angle ABC:
Since A, B, and C are consecutive vertices, they form one of the interior angles of the regular polygon. The regular polygon has 20 sides, so we can use the formula:
Angle ABC = (20-2) * 180° / 20
Simplifying this equation will give us the value of angle ABC.
(b) Angle ACD:
Again, since A, C, and D are consecutive vertices, they form another interior angle of the regular polygon. Let's use the same formula as above:
Angle ACD = (20-2) * 180° / 20
Simplifying this equation will give us the value of angle ACD.
(c) Angle ABD:
To calculate angle ABD, we can use the fact that angle ABD is the sum of angles ABC and ACD, as they are consecutive angles on the same side of the line BD.
Angle ABD = Angle ABC + Angle ACD
By substituting the values of angles ABC and ACD that we calculated earlier, we can find the value of angle ABD.
So, plug in the values into the formulas, simplify the equations, and you'll have the values of the angles ABC, ACD, and ABD in the regular polygon with 20 sides.