Question

Find the angle measure x in the following figures.

(a)	(b)
(c)	(d)

Answer 1

(a)

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)

From the figure, it can be concluded that,

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, 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 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°