Question

Find m angle d for m angle b = 65
The figure is not drawn to scale

Answer 1

Answer:

Denote O as center of circle, draw OA, OC.

As property of tangent line from outside of circle (angle OAD = angle OCD = 90 deg):

=> AOC + D = 180

Moreover, angle  AOC = 2 x angle B = 2 x 65 = 130

=> D = 180 - 130 = 50 deg

Hope this helps!

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Answer 2

The measure of the angle d for m angle b = 65 in the figure of circle and quadrilateral is 50 degrees. Option A is correct.

What is a measure of angle?

The measure of angle between the two points of a ray or line is the measure of rotation between these two points. The angles are measured in degrees or radians.  

The figure given in the problem contained a circle and a quadrilateral.

In this figure, the measure of the angle b is,

$m\angle d =65^o$

Here, the two tangent lines AD and DC cuts the circle at point A and C respectively.

Let the center of the circle is O. Thus the angle b is equal to the angle AOC by the tangent line theorem as,

$\angle O =2m\angle b=130 ^o$

The sum of angle AOC and the angle D is equal to 180 degrees. Therefore,

$\angle AOC+m\angle d=180\\130++m\angle d=180\\m\angle d=180-130\\m\angle d=50^o$

Hence, the measure of the angle d for m angle b = 65 in the figure of circle and quadrilateral is 50 degrees. Option A is correct.

Learn more about the measure of angle here;

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