Question

Find the value of z.

Answer 1

Applying the angle of intersecting chords theorem, the value of z is: D. 100.

What is the Angle of Intersecting Chords Theorem?

According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.

Applying the angle of intersecting chords theorem, let's find x first:

73 = 1/2(96 + x)

Multiply both sides by 2

2 × (73) = 1/2(96 + x) × 2

146 = 96 + x

Subtract both sides by 96

146 - 96 = 96 + x - 96

50 = x

x = 50°

Therefore:

x + z + 96 + 114 = 360° [full circle measure]

Plug in the value of x

50 + z + 96 + 114 = 360

z + 260 = 360

Subtract both sides by 260

z + 260 - 260 = 360 - 260

z = 100°

The answer is: D. 100°.

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