Find the angle measure x in the following figures

A.


B.


C.


D.

A. We know that,


Sum of the measures of all interior angles of a quadrilateral is 360o.


Therefore, in the given quadrilateral,


50° + 130° + 120° + x = 360°


300° + x = 360°


x = 60°


B. We know that, angle sum of quadrilateral = 3600


90o + a = 180o (Linear pair)


a = 180o – 90o


= 90o


Sum of the measures of all interior angles of a quadrilateral is 360o.


Therefore, in the given quadrilateral,


60° + 70° + x + 90° = 360°


220° + x = 360°


x = 140°


C. From the figure,


70 + a = 180° (Linear pair)


a = 110°


60° + b = 180° (Linear pair)


b = 120°


Sum of the measures of all interior angles of a pentagon is 540o


Therefore, in the given pentagon,


120° + 110° + 30° + x + x = 540°


260° + 2x = 540°


2x = 280°


x = 140°


D. Sum of the measures of all interior angles of a pentagon is 540o


5x = 540°


x = 108°


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