You focus your camera on a circular fountain. Your camera is at the vertex of the angel formed by tangents to the fountain. You estimate that the angle is 44°. What is the measure of the arc of the circular basin of the fountain that will be in the photograph?

The measure of the arc of the circular basin of the fountain that will be in the photograph is; 136°

To answer this question, we need to understand the angle of intersecting secant theorem which state that;

If two lines intersect outside a circle, then the measure of the angle formed by the two lines is half of the positive difference of the measures of the intercepted arcs.

Thus;

θ = ½(x2 - x1)

Where:

• x2 is large angle
• x1 is small angle
• θ is measure of the Angle formed by the two lines

Now, we are given θ = 44°

Now the measure of the arc of the circular basin will be the smaller angle x1.

• However, the sum of the large and small angle is 360° and so large angle is 360 - x1.

Thus;

44 = ½(360 - x - x)

2 × 44 = 360 - 2x

88 = 360 - 2x

360 - 88 = 2x

2x = 272

x = 272/2

x = 136°

Read more about angle of intersecting secanttheorem at; brainly.com/question/1626547

Answer:

The measure of the arc of the circular basin = 136°

Step-by-step explanation:

The measure of an angle formed when two line intercepts outside a circle is half the difference of the measure of the intercepted arcs.

Mathematically, the is represented as:

Measure of an angle = 1/2(big angle - Small angle)

This values are given in the question

Measure of an angle = Measure of angle formed by tangents to the fountain = 44°

big angle is represented by = 360°-x

small angle is represented by = x

Therefore, we have

44° = 1/2( 360° - x -x)

44° = 1/2(360° - 2x)

Cross multiply

44° × 2 = 360° - 2x

88° = 360° - 2x

88° - 360° = - 2x

-272° = -2x

x = -272/-2

x = 136°

The measure of the arc of the circular basin = 136°