Question

1. which of the following is the contrapositive of the conditional (\if... then\) statement below? if the radius of a circle is perpendicular to a line at a point on the circle, then the line is tangent to the circle. a. if a line is not tangent to a circle, then the radius is not perpendicular to the line. b. if a line is tangent to a circle, then the radius of the circle is perpendicular to the line at a point on that circle. c. if the line is perpendicular to a radius of a circle at a point on that circle, then the line is tangent to the circle. d. if the line is not tangent to a circle, then the radius of a circle is not perpendicular to a line at a point on the circle. 4. find the values of x and y, and label the measures of each angle. (3x + 32)° (y - 62)° 7x° 2y/3°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(2y=\ 3x + 32\).

Step2: Use linear - pair property

Adjacent angles on a straight - line are supplementary. So, \(7x+(y - 62)=180\), which can be rewritten as \(y=180 + 62-7x=242 - 7x\).

Step3: Substitute \(y\) into the first equation

Substitute \(y = 242-7x\) into \(2y=3x + 32\). We get \(2(242-7x)=3x + 32\).
Expand the left - hand side: \(484-14x=3x + 32\).

Step4: Solve for \(x\)

Add \(14x\) to both sides: \(484=3x + 14x+32\), which simplifies to \(484 = 17x+32\).
Subtract 32 from both sides: \(17x=484 - 32=452\).
Then \(x=\frac{452}{17}\approx26.59\).

Step5: Solve for \(y\)

Substitute \(x\) into \(y = 242-7x\). \(y=242-7\times\frac{452}{17}=\frac{242\times17-7\times452}{17}=\frac{4114 - 3164}{17}=\frac{950}{17}\approx55.88\).

Answer:

\(x=\frac{452}{17},y=\frac{950}{17}\)