Question

What is the value of s?
35
55
70
90

Answer 1

35 degrees. Hope this helps!

Answer 2

A. 35.

Explanation:

Let x represent the complementary angle of 's'.

We have been given an image of a circle. We are asked to find the value of 's' for our given circle.

Upon looking at our given circle, we can see that angle 's' is an inscribed angle of our given circle.

We know that an inscribed angle formed across diameter of a circle is always a 90 degree or right angle, so the measure of intercepted arc of angle x and angle 's' will be 180 degrees.

`\text{Intercepted arc of x}+\text{Intercepted arc of s}=180^(\circ)`

`110^(\circ)+\text{Intercepted arc of s}=180^(\circ)`

`110^(\circ)-110^(\circ)+\text{Intercepted arc of s}=180^(\circ)-110^(\circ)`

`\text{Intercepted arc of s}=70^(\circ)`

We know that an inscribed angle is half the measure of its intercepted arc. So we can set an equation as:

`m\angle s=(1)/(2)* \text{(Measure of intercepted arc of s})`

`m\angle s=(1)/(2)* 70^(\circ)`

`m\angle s=35^(\circ)`

Therefore, te value of 's' is 35 and option A is the correct choice.