The measure of m∠XBC=(3p-6)°=(3·47-6)°=135°.
What is meant by geometric mean theorem?
- The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem, which is a consequence of elementary geometry.
- It claims that the altitude is equal to the geometric mean of the two segments.
- The later version provides a method for squaring a rectangle using a ruler and compass, which entails creating a square with the same area as the rectangle in question.
- Since the inverse of Thales' theorem guarantees that the hypotenuse of the right angled triangle is the diameter of its circumcircle, the theorem may also be seen as a specific example of the intersecting chords theorem for a circle.
Given data :
m∠XBC = m∠BAC + m∠BCA,
Now if : m∠XBC=(3p-6)°: m∠BAC=(p+4)°: m∠BCA=84°,
then we get the equation :
3p-6=p+4+84
(option 2), 3p-6=p+88
(option 3), 3p-p-6=p-p+88,2p-6=88
(option 4), 2p-6+6=88+6,2p=94
(option 5), p=47.
Then m∠XBC=(3p-6)°=(3·47-6)°=135°.
Learn more about geometric mean theorem refer to :
https://brainly.com/question/10612854
#SPJ1
