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43 votes
43 votes
Find the value of z.

Find the value of z.-example-1
User Lee Stott
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1 Answer

8 votes
8 votes

Answer:

z = 110°

Explanation:

Angles z and the one marked 70° form an linear pair, hence are supplementary.

z = 180° -70° = 110°

Angles where chords cross

The angle made by two chords is half the sum of the arcs intercepted by those chords. Here, that means ...

70° = 1/2(60° +x) ⇒ x = 140° -60° = 80°

The arc w completes the circle of 360°, so we have ...

w +x +79° +60° = 360° ⇒ w = 360° -219° = 141°

Finally, z is the average of w and 79°:

z = (w +79°)/2 = (141° +79°)/2 = 110° . . . as above

User Mohammad AlQanneh
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3.4k points