The circles below are concentric
What is the measure of the angle formed by the two secants?
What is the value of x?

Given:

Intercepted arcs of small circle:

78° and x°

Intercepted arcs of large circle:

57° and 121°

To find:

The measure of angle formed by two secants and the value of x.

Solution:

Consider a large circle:

The angle made by two secants intersecting outside a circle is half the difference between the measure of intercepted arcs.

The measure of the angle formed by two secants is 32°.

Two circles are concentric circles.

Therefore 32° is also the angle made by small circle arcs.

Multiply by 2 on both sides.

Add 78° on both sides.

The value of x is 124.

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