Answer:
Step-by-step explanation:
4). m(arc GJ) = 90°
5). m(arc HI) = m(arc JH) - m(arc JI)
= 180° - 151°
= 29°
6). m(arc HIJ) = 180°
7). m(arc GJI) = m(arc GJ) + m(arc JI)
= 90° + 151°
= 241°
8). m(arc GHJ) = m(arc GH) + m(arc HI) + m(arc IJ)
= 90° + 29° + 151°
= 170°
9). m(arc GJH) = 360° - m(arc GH)
= 360° - 90°
= 270°
10). m(arc HGJ) = 180°
11). m(arc GH) = 90°
12). m(arc GHI) = m(arc GH) + m(arc HI)
= 90° + 29°
= 119°
13). m(arc HJI) = 360° - m(arc HI)
= 360° - 29°
= 331°
14). m(arc JHI) = m(arc JH) + m(arc HI)
= 180° + 29°
= 209°
15). m(arc JIG) = 360° - m(arc JG)
= 360° - 90°
= 270°
The measures of each arc in the circle shown in the diagram are:
4. [tex]\mathbf{\widehat{GJ} = 90^{\circ}}[/tex] (right angle)
5. [tex]\mathbf{\widehat{HI} = 29^{\circ}}[/tex]
6. [tex]\mathbf{\widehat{HIJ} = 180^{\circ}}[/tex] (semicircle = 180°)
7. [tex]\mathbf{\widehat{GJI} = 241^{\circ}}[/tex]
8. [tex]\mathbf{\widehat{GHJ} = 270^{\circ}}[/tex]
9. [tex]\mathbf{\widehat{GJH} = 270^{\circ}}[/tex]
10. [tex]\mathbf{\widehat{HGJ} = 180^{\circ}}[/tex] (semicircle = 180°)
11. [tex]\mathbf{\widehat{GH} = 90^{\circ}}[/tex] (right angle)
12. [tex]\mathbf{\widehat{GHI} = 119^{\circ}}[/tex]
13. [tex]\mathbf{\widehat{HJI} = 331^{\circ}}[/tex]
14. [tex]\mathbf{\widehat{JHI} = 209^{\circ}}[/tex]
15. [tex]\mathbf{\widehat{JIG} = 270^{\circ}}[/tex]
Recall:
Given circle with center B, thus:
4. [tex]\mathbf{\widehat{GJ} = 90^{\circ}}[/tex] (right angle)
5. [tex]\widehat{JI} = 151^{\circ}[/tex] (given)
[tex]\widehat{JI} + \widehat{HI} = 180^{\circ}[/tex] (semicircle = 180°)
[tex]151 + \widehat{HI} = 180^{\circ}\\\\\widehat{HI} = 180 - 151\\\\\mathbf{\widehat{HI} = 29^{\circ}}[/tex]
6. [tex]\mathbf{\widehat{HIJ} = 180^{\circ}}[/tex] (semicircle = 180°)
7. [tex]\widehat{GJI} = \widehat{GJ} + \widehat{JI}[/tex]
[tex]\widehat{GJI} =90 + 151\\\\\mathbf{\widehat{GJI} = 241^{\circ}}[/tex]
8. [tex]\widehat{GHJ} = \widehat{GH} + \widehat{HIJ}[/tex]
[tex]\widehat{GHJ} =90 + 180\\\\\mathbf{\widehat{GHJ} = 270^{\circ}}[/tex]
9. [tex]\widehat{GJH} = \widehat{GJ} + \widehat{HIJ}[/tex]
[tex]\widehat{GJH} =90 + 180\\\\\mathbf{\widehat{GJH} = 270^{\circ}}[/tex]
10. [tex]\mathbf{\widehat{HGJ} = 180^{\circ}}[/tex] (semicircle = 180°)
11. [tex]\mathbf{\widehat{GH} = 90^{\circ}}[/tex] (right angle)
12. [tex]\widehat{GHI} = \widehat{GH} + \widehat{HI}[/tex]
[tex]\widehat{GHI} =90 + 29\\\\\mathbf{\widehat{GHI} = 119^{\circ}}[/tex]
13. [tex]\widehat{HJI} = 360 - \widehat{HI}[/tex]
[tex]\widehat{HJI} =360 - 29\\\\\mathbf{\widehat{HJI} = 331^{\circ}}[/tex]
14. [tex]\widehat{JHI} = 360 - \widehat{JI}[/tex]
[tex]\widehat{JHI} =360 - 151\\\\\mathbf{\widehat{JHI} = 209^{\circ}}[/tex]
15. [tex]\widehat{JIG} = 360 - \widehat{GJ}[/tex]
[tex]\widehat{JIG} =360 - 90\\\\\mathbf{\widehat{JIG} = 270^{\circ}}[/tex]
Learn more here:
https://brainly.com/question/23535384
