Question

Im not understanding how to answer this problem Find the measure of each angle in the following figure.

Answer 1

The sum of the internal angles of a polygon of n sides is given by:

S = (n-2)*180°

The polygon ABCDEF has 6 sides, then the sum of its internal angles must be:

S = (6-2)*180° = 4*180° = 720°

Therefore, we have:

x° + 126° + 124° + (x + 8)° + (x - 34)° +130° = 720

x° + x° + 8° + x° - 34° + 380° = 720°

3x° + 354° = 720°

3x° = 366°

x = 122°

Then the answer is:

`\begin{gathered} m\angle A=x\degree=122\degree \\ m\angle B=126\degree \\ m\angle C=124\degree \\ m\angle D=(x+8)\degree=(122+8)\degree=130\degree \\ m\angle E=(x-34)\degree=(122-34)\degree=88\degree \\ m\angle F=130\degree \end{gathered}`