Question

find the value of each variable in the circle to the right. the dot represents the center of the circle.

Answer 1

We have been given an image of a circle. We are asked to find the value of each variable.

We can see that angle b corresponds to diameter of circle. We know that the measure of an angle that is inscribed to the diameter of a circle is 90 degrees . Therefore, the value of b will be 90.

we can see that angle is an inscribed angle of arc 99 degrees. We know that measure of an inscribed angle is half the measure of inscribed arc.

`a=(1)/(2)\cdot 99`

`a=49.5`

Therefore, the value of a is 49.5 units.

We know that measure of all angles of a triangle is 180 degrees. The measure of 3rd angle will be half the measure of c, so we can set an equation as:

`a+b+(1)/(2)c=180`

`49.5+90+(1)/(2)c=180`

`139.5+(1)/(2)c=180`

`139.5-139.5+(1)/(2)c=180-139.5`

`(1)/(2)c=40.5`

`(1)/(2)c\cdot 2=40.5\cdot 2`

`c=81`

Therefore, the value of c is 81.