Respuesta :
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°
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 secant theorem at; https://brainly.com/question/1626547
