Question

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.

Answer 1

Question 1)
`x=6\°`

Question 2)
`x=9\°`

Question 4)
`arc\ BD=12\°`

Explanation:

Question 1) we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

so

In this problem

`124\°=(1)/(2)(arc\ RQ+arc\ SC)`

substitute the values and solve for x

`124\°=(1)/(2)(197\°+(9x-3)\°)`

`248\°=194\°+9x`

`9x=248\°-194\°`

`9x=54\°`

`x=6\°`

Question 2) we know that

The measurement of the external angle is the semi-difference of the arcs it comprises

so

in this problem

`(5x-5)\°=(1)/(2)(190\°-(13x-7))`

solve for x

`(10x-10)\°=(197\°-13x)`

`(13x+10x)\°=(197\°+10\°)`

`23x\°=207\°`

`x=9\°`

Question 4) we know that

The measurement of the external angle is the semi-difference of the arcs it comprises

so

in this problem

`(6x-12)\°=(1)/(2)((-12+21x)\°-(12x-24))`

solve for x

`(12x-24)\°=((-12+21x)\°-(12x-24))`

`(24x-48)\°=(-12+21x)\°`

`(24x-21x)\°=(-12+48)\°`

`3x=36\°`

`x=12\°`

Find the measure of arc BD

`arc\ BD=12x-24=12(3)-24=12\°`