Question

Can someone please tell me the answers but also explain how to do it? Thank you

Answer 1

8: 90 degrees, 9: 165 degrees, 6: 81 degrees, 7: angles in the same segment are equal

Explanation:

For question 8:

Notice how the line AB just barely touches the edge of the circle. We call this kind of line a tangent. The point O is at the center of the circle so the line OB is a radius. The angle between a tangent and a radius is always 90 degrees, so ABO is 90 degrees.

For question 9:

By the exact same logic as 8, ACO is also 90 degrees. The sum of interior angles in a 4 sided shape (a quadrilateral) is always 360 degrees. This means that 15 + 90 + 90 + x = 360 = 195 + x so x = 360 - 195 = 165

For question 6/7:

We use the theorem that the angles in the same segment are equal. This means that a is 81 degrees.