Find the value of z.

Mathematics

1 answer:

AVprozaik [17]2 years ago

8 0

Answer:

z = 110°

Step-by-step explanation:

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

z = 180° -70° = 110°

<h3>Angles where chords cross</h3>

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

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