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For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.
Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:
The opposite angles in a parallelogram are congruent, therefore:
The sum of internal angles is 360º, therefore we have:
The value of x is 33º, the value of y is 38º and the value of z is 109º.
The length of CS is 11.0
Explanation:
Given that the length of the tangent AR is 12
The length of SR is 7.7
To find: The length of CS
The<u> tangent secant theorem</u> states that "if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant’s external part and the entire secant."
Applying the tangent secant theorem, we have,
Rewriting the above equation, we get,
Substituting the values, we get,
Simplifying, we have,
Subtracting both sides by 59.29, we get,
Dividing both sides by 7.7, we have,
Rounding off to the nearest tenth, we get,
Thus, the length of CS is 11.0