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 360^{o}.

Therefore, in the given quadrilateral,

50° + 130° + 120° + x = 360°

300° + x = 360°

x = 60°

B. We know that, angle sum of quadrilateral = 360^{0}

90^{o} + a = 180^{o} (Linear pair)

a = 180^{o} – 90^{o}

= 90^{o}

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

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 540^{o}

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^{o}

5x = 540°

x = 108°

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