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In the circle below,  m∠M=(6x−10)∘,  m∠T=(5x−3)∘,  and  m∠H=(4x−2)∘.  Find  x (Note that the diagram may not be drawn to scale.) a x=6 b x=13  c x=4 d x=1  x=7

In the circle below,  m∠M=(6x−10)∘,  m∠T=(5x−3)∘,  and  m∠H=(4x−2)∘.  Find  x (Note that the diagram may not be drawn to scale.) a x=6 b x=13  c x=4 d x=1  x=7

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
In the circle below,  m∠M=(6x−10)∘,  m∠T=(5x−3)∘,  and  m∠H=(4x−2)∘.  Find  x
(Note that the diagram may not be drawn to scale.)
a x=6
b x=13


 c x=4


d x=1


 x=7
The image shows a circle with four points on its circumference labeled \(M\), \(A\), \(H\), and \(T\). These points are connected by chords, forming a quadrilateral inside the circle. - The point \(M\) is connected to \(A\) and \(H\). - The point \(A\) is connected to \(T\). - The point \(H\) is connected to \(T\). - The point \(T\) is connected to \(M\). The lines \(MA\), \(AT\), \(TH\), and \(HM\) form the sides of the quadrilateral. Additionally, there are two diagonals: \(MT\) and \(AH\). This arrangement illustrates a cyclic quadrilateral, where all vertices lie on the circumference of a circle. In such quadrilaterals, opposite angles are supplementary. This figure is often used to demonstrate properties related to circle theorems in geometry.
Transcribed Image Text:The image shows a circle with four points on its circumference labeled \(M\), \(A\), \(H\), and \(T\). These points are connected by chords, forming a quadrilateral inside the circle. - The point \(M\) is connected to \(A\) and \(H\). - The point \(A\) is connected to \(T\). - The point \(H\) is connected to \(T\). - The point \(T\) is connected to \(M\). The lines \(MA\), \(AT\), \(TH\), and \(HM\) form the sides of the quadrilateral. Additionally, there are two diagonals: \(MT\) and \(AH\). This arrangement illustrates a cyclic quadrilateral, where all vertices lie on the circumference of a circle. In such quadrilaterals, opposite angles are supplementary. This figure is often used to demonstrate properties related to circle theorems in geometry.
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