Mathematics

Grade9

Easy

Question

# If two chords intersect inside a circle, then the measure of each angle is one half the _____________ of the measures of the arcs intercepted by the angle and its vertical angle.

- Difference
- Sum
- Product
- None of the above

Hint:

### According to the Angles of intersecting chords theorem, we can say that "If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.". Here, we have to fill the blank using this theorem.

## The correct answer is: Sum

### In the question there is a blank which we have to fill using the given options.

According to the Angles of intersecting chords theorem, we can say that

If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

So, the answer will be sum.

Therefore, the correct option is b, i.e., sum.

Vertical angles are a pair of opposite angles which are formed when two lines intersect with each other.

Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.

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