danielahchf
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Angles ABC, BCD, CDA and DAB are inscribed angles and form intercepted arcs.

(a) find the value of x

(b) find the value of y

(c) find the value of z

Angles ABC BCD CDA and DAB are inscribed angles and form intercepted arcs a find the value of x b find the value of y c find the value of z class=

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sqdancefan

Answer:

  • x = 120°
  • y = 80°
  • z = 100°

Step-by-step explanation:

The rule required here is that the measure of an inscribed angle is half the measure of the arc it intercepts.

(a) ∠BCD = 90°, so arc BAD is ...

... x + 60° = 2×90°

... x = 180° -60° = 120°

(b) ∠ABC = 100°, so arc ADC is ...

... x + y = 2×100°

... y = 200° -120° = 80°

(c) From part A, we know that arc BAD = 180°, so arc BCD = 180° (since they add to make 360°). Arc BCD is ...

... y + z = 180°

... z = 180° -80° = 100°

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