A. Find x + y + z

B. Find x + y + z + w

A. We know that,

x + 90° = 180° (Linear pair)

x = 90°

z + 30° = 180° (Linear pair)

z = 150°

y = 90° + 30° (Exterior angle theorem)

y = 120°

x + y + z = 90° + 120° + 150°

= 360°

We know that angle sum of quadrilateral 360^{o}. Therefore, in the given quadrilateral,

a + 60° + 80° + 120° = 360°

a + 260° = 360°

a = 100°

x + 120° = 180° (Linear pair)

x = 60°

y + 80° = 180° (Linear pair)

y = 100°

z + 60° = 180° (Linear pair)

z = 120°

w + 100° = 180° (Linear pair)

w = 80°

Sum of the measures of all interior angles = x + y + z + w

= 60° + 100° + 120° + 80°

= 360°

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