Mathematics: The measure of arc XY is 85 degrees. The measure of arc WZ is 25 degrees. What is the measure of angle 3?

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The measure of arc XY is 85 degrees. The measure

Ответ:

Machuco127

09.07.2021

Mathematics

Given:

Consider the below figure attached with this question.

To find:

The measure of angle 3.

Solution:

According to intersecting secant theorem, if two secants of a circle intersect each other outside the circle, then the angle on the intersection is half of the difference of the intercepted arc.

$\text{Angle on intersection}=\dfrac{1}{2}(\text{Major arc}-\text{Minor arc})$

Using the intersecting secant theorem, we get

$m\angle 3=\dfrac{1}{2}(m(arcXY)-m(arcWZ))$

$m\angle 3=\dfrac{1}{2}(85^\circ-25^\circ)$

$m\angle 3=\dfrac{1}{2}(60^\circ)$

$m\angle 3=30^\circ$

Therefore, the measure of angle 3 is 30 degrees.

The measure of arc XY is 85 degrees. The measure of arc WZ is 25 degrees. What is the measure of ang

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The measure of arc XY is 85 degrees. The measure of arc WZ is 25 degrees. What is the measure of angle 3?

Ответ:

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