(a) Sum of the measures of all interior angles of a quadrilateral is 360. Therefore, in the given quadrilateral,
50° + 130° + 120° + x = 360°
300° + x = 360°
x = 60°
(b)
From the figure, it can be concluded that,
90 + a = 180 (Linear pair)
a = 180 − 90 = 90
Sum of the measures of all interior angles of a quadrilateral is 360. Therefore, in the given quadrilateral,
60° + 70° + x + 90° = 360°
220° + x = 360°
x = 140°
(c)
From the figure, it can be concluded that,
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 540.
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 540.
5x = 540°
x = 108°
