Mathematics
Grade9
Easy

Question

The measure of the unknown angle x is ________.

  1. 91°
  2. 163°
  3. 107°
  4. Cannot determine

hintHint:

s u m space o f space a l l space i n t e r i o r space a n g l e s space o f space a space p e n t a g o n space equals space left parenthesis 5 minus 2 right parenthesis cross times 180 to the power of o
s u m space o f space a l l space i n t e r i o r space a n g l e s space o f space a space p e n t a g o n space i s space 540 degree

The correct answer is: 107°


    Here, 72° and angle A form a linear pair so  72° + angle A = 180 to the power of o
    So angle A = 180° - 72° = 108°
    The sum of all interior angles of a pentagon is 540°
    So, 90° + x° + 127° + 108° + 108° = 540°
    x = 107°.

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