Question

Please help! I thought it was 90º but it says thats wrong.

Answer 1

Explanation:

I posted a picture at the bottom of the post that you need to look at in order to understand this problem. I labeled everything inside that circle and then created a triangle. That triangle is made up of 3 sides that are all the same length, and that length is the length of the radius. By definition, if a triangle has all 3 of its sides the same length, it is equilateral. It is also equiangular. That means that every angle inside that triangle measures 60 degrees. The central angle, the one that comes off the center, intercepts an arc. The arc measure is the same measure as this angle, so the intercepted arc measures 60 degrees. To find the measure of the angle in question, the one you need that is labeled with a pink θ, has a rule that says the angle is going to be half the measure of the intercepted arc. That means that your angle is going to measure 30 degrees.

Answer 2

30°

Explanation:

As the chord has same length of radius, the chord and the two radius form a equilateral triangle. Each angle of triangle is 60.So the chord subtended at the center is 60. So the angle subtended at the remaining part of the circle = 30°

The measure of angle between the tangent and chord = 30 {Alternate segment theorem}