The value of <em>x</em> where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is <em>x </em>= 23°
<h3>What is the exterior angles theorem?</h3>
The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
The given parameters are;
Points on the circle are; ABCD
Straight lines = AOBE and DCE
Segment CO = Segment CE
∠AOD = 69°
∠CEO = x°
∠OCD = ∠ODC base angles of isosceles triangle
69° = ∠x° + ∠ODC exterior angle of a triangle
∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)
180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)
x° + 69° - 2×∠ODC = 0
∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)
69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)
69° = 3·x°
x = 69° ÷ 3 = 23°
Learn more about angles in a triangle here:
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A square is made up of 4 equal sides all you would have to do to find the perimeter is divided 86 by 4 and that equals 21.5
21.5 should be your answer
Answer:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
Make an proportion 24 trucks/8 hours = ? trucks/1 hour, which the answer is 24/8 = 3, so three trucks an hour, but that doesn't seem to be a choice.... hmm