Solving Unknown Measures Using an Inscribed Angle

INSCRIBED ANGLE
It refers to an angle whose vertex is on a circle and whose sides contains chords of the circle.

CIRCLE refers to a set of all points on a plane that are equidistant from a given point called the center.
ANGLE is a figure formed by two lines.
CHORD is a straight line whose endpoints both lie on the circle.

In circle P shown below, angle ABC is an inscribed angle and arc AC is its intercepted arc.

ARC is a part of a circle (a curve line).
INTERCEPTED ARC is an arc opposite formed opposite to an inscribed angle.

PROPERTIES OF AN INSCRIBED ANGLE:

1. It is said to be that the measure of an inscribed angle is half the measure of its intercepted arc.
   In circle P, m<ABC - 1/2 measure of arc AC.

2. If two inscribed angles intercept the same arc, then the angles are congruent.

3. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

4. An angle inscribed in a semicircle is a right angle.

EXAMPLES
Find each measures given the figure attached below.

1. measure of arc AB

<APB is a central angle.
Measure of arc AB - m<APB
Therefore, measure of arc AB is 70 degrees.

1. measure of <ADB

The intercepted arc of <ADB is arcAB.
Since, measure of arc AB is 70 degrees, m<ADB = 1/2 (measure of arc AB) = 1/2 (70 degrees) = 35 degrees.

1. measure of <ACD
   

That would be all for today. Thanks for now and have a great day ahead!