Before we begin, let’s state a few important theorems.

**THEOREM:** If two angles inscribed in a circle intercept the same arc, then they are equal to each other.

**THEOREM:** If an angle inside a circle intercepts a diameter, then the angle has a measure of \(90^\circ \).

Now let’s use these theorems to find the values of some angles!

**EXAMPLE:** Find the measure of the angle indicated.

**SOLUTION:** First we see that \(\measuredangle DNC\) and \(\measuredangle DEC\) both intercept the same arc. So, by our first theorem, we know that \(\measuredangle DNC = \measuredangle DEC\). And since \(\measuredangle DNC = 37^\circ \), we conclude that \(\measuredangle DEC = 37^\circ \).

Next, since \(\measuredangle EDC\) intercepts a diameter of the circle, we can conclude, by our second theorem, that \(\measuredangle EDC = 90^\circ \).

So two of the angles in triangle \(EDC\) are \(90^\circ \) and \(37^\circ \). Then, by using the fact that the tree angles of a triangle must sum to \(180^\circ \), we know that the measure of the desired angle is \(53^\circ \).

**EXAMPLE:** Find the measure of the indicated angle.

**SOLUTION:** Since \(\measuredangle NBM\) and \(\measuredangle NLM\) intercept the same arc, they are equal, so that \(\measuredangle NLM = 52^\circ \). Next, since \(\measuredangle NML\) intersects a diameter of the circle, we know that \(\measuredangle NML = 90^\circ \). Then since two of the angles of triangle \(LMN\) are \(90^\circ \) and \(52^\circ \), we know that the desired angle must be \(38^\circ \), by the fact that the three angles of a triangle must sum to \(180^\circ \). Solution: The desired angle is \(38^\circ \).

Below you can **download** some **free** math worksheets and practice.

State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.

This free worksheet contains 10 assignments each with 24 questions with answers.

**Example of one question:**

**Watch bellow how to solve this example:**

Find the measure of the arc or angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.

**Example of one question:**

**Watch bellow how to solve this example:**

Solve for x and y.

This free worksheet contains 10 assignments each with 24 questions with answers.

**Example of one question:**

**Watch bellow how to solve this example:**