Answer:
The angle Matt drew = 180°
Step-by-step explanation:
The total angle formed by the 8 angles Matt drew in the circle equals 360° because one revolution of a circle is the same as the angle about a point which equals 360°.
Let the equal angles drawn = x
x + x + x + x + x + x + x + x = 360°
8 × x = 360°
8x = 360
x = 45°
∴ each angle drawn = 45°
Next, we are told that Matt drew another angle that has the same measurement as four (4) of the sections (angles) in the circle.
Finding the measure of this angle:
1 section in the circle = 45 (<em>shown above</em>)
∴ 4 sections = 45 × 4 = 180°
∴ The angle Matt drew = 180°
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
<h3>What is the Angle of Intersecting Chords Theorem?</h3>
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°.
Learn more about the angle of intersecting chords theorem on:
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Answer:
Just mark the upward part of X axis.
Answer:
D
Step-by-step explanation:
Circumference of circle = 2πr
r = 9cm
Circumference of circle = 2×9×3.142
Circumference of circle = 56.5cm
Answer: 88.74
Step-by-step explanation:
