Q:

20 Points! These need to be answered Today, so please help. This could make or break my grade. Answer all 3. I only have ONE shot at this so please make sure the answers are correct.

Accepted Solution

A:
Answer:Question 1) [tex]x=6\°[/tex]Question 2) [tex]x=9\°[/tex]Question 4) [tex]arc\ BD=12\°[/tex]Step-by-step explanation:Question 1) we know thatThe measure of the interior angle is the semi-sum of the arcs comprising it and its oppositesoIn this problem[tex]124\°=\frac{1}{2}(arc\ RQ+arc\ SC)[/tex]substitute the values and solve for x[tex]124\°=\frac{1}{2}(197\°+(9x-3)\°)[/tex][tex]248\°=194\°+9x[/tex][tex]9x=248\°-194\°[/tex][tex]9x=54\°[/tex][tex]x=6\°[/tex]Question 2) we know thatThe measurement of the external angle is the semi-difference of the arcs it comprisessoin this problem[tex](5x-5)\°=\frac{1}{2}(190\°-(13x-7))[/tex]solve for x [tex](10x-10)\°=(197\°-13x)[/tex]  [tex](13x+10x)\°=(197\°+10\°)[/tex][tex]23x\°=207\°[/tex][tex]x=9\°[/tex]Question 4) we know thatThe measurement of the external angle is the semi-difference of the arcs it comprisessoin this problem[tex](6x-12)\°=\frac{1}{2}((-12+21x)\°-(12x-24))[/tex]solve for x[tex](12x-24)\°=((-12+21x)\°-(12x-24))[/tex][tex](24x-48)\°=(-12+21x)\°[/tex][tex](24x-21x)\°=(-12+48)\°[/tex][tex]3x=36\°[/tex][tex]x=12\°[/tex]Find the measure of arc BD[tex]arc\ BD=12x-24=12(3)-24=12\°[/tex]