Answer:
Part 1) The measures of the angles are
[tex](260/15)\°[/tex]
[tex](606/15)\°[/tex]
[tex](484/15)\°[/tex]
Part 2) The measure of the angles are
[tex](315/12)\°[/tex]
[tex](985/12)\°[/tex]
[tex](860/12)\°[/tex]
Step-by-step explanation:
Part 1) we know that
[tex](5x-8)+(6x+10)+(4x+12)=90\°[/tex]
solve for x
[tex]15x+14=90\°[/tex]
[tex]15x=90\°-14\°[/tex]
[tex]x=(76/15)\°[/tex]
The measure of the angles are
[tex](5(76/15)-8)=(260/15)\°[/tex]
[tex](6(76/15)+10)=(606/15)\°[/tex]
[tex](4(76/15)+12)=(484/15)\°[/tex]
Part 2) we know that
[tex](3x-20)+(5x+5)+(4x+10)=180\°[/tex]
solve for x
[tex]12x-5=180\°[/tex]
[tex]12x=180\°+5\°[/tex]
[tex]x=(185/12)\°[/tex]
The measure of the angles are
[tex](3(185/12)-20)=(315/12)\°[/tex]
[tex](5(185/12)+5)=(985/12)\°[/tex]
[tex](4(185/12)+10)=(860/12)\°[/tex]
